{"id":20700,"date":"2024-03-20T21:19:49","date_gmt":"2024-03-20T21:19:49","guid":{"rendered":"https:\/\/science-hub.click\/%E9%9B%86%E5%90%88%E3%81%AE%E5%8D%8A%E7%92%B0-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-03-20T21:19:49","modified_gmt":"2024-03-20T21:19:49","slug":"%E9%9B%86%E5%90%88%E3%81%AE%E5%8D%8A%E7%92%B0-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=20700","title":{"rendered":"\u96c6\u5408\u306e\u534a\u74b0 &#8211; \u5b9a\u7fa9"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p><b>\u30bb\u30c3\u30c8\u306e\u30bb\u30df\u30ea\u30f3\u30b0<\/b>(\u901a\u5e38\u306f<b>semiring<\/b>\u3068\u7701\u7565\u3055\u308c\u307e\u3059) \u306f\u3001\u30bb\u30c3\u30c8\u306e\u30ea\u30f3\u30b0\u3092\u7c21\u5358\u306b\u69cb\u7bc9\u3067\u304d\u308b\u30bb\u30c3\u30c8<i>X<\/i>\u306e\u90e8\u5206\u306e\u30af\u30e9\u30b9\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u53e4\u5178\u7684\u306a\u6e2c\u5b9a\u69cb\u9020\u3092\u958b\u59cb\u3059\u308b\u306e\u306b\u4fbf\u5229\u306a\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u3067\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u96c6\u5408\u306e\u534a\u74b0 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/dO1T5-N3k1U\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u610f\u5473<\/h2><div><p><strong>\u5b9a\u7fa9<\/strong><span>\u2014<\/span><b>\u96c6\u5408\u306e\u534a\u74b0\u306f<\/b><span><a href=\"https:\/\/science-hub.click\/?p=57227\">\u96c6\u5408<\/a><\/span>\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\mathcal S} $$<\/div>\u4ee5\u4e0b\u3092\u6e80\u305f\u3059\u96c6\u5408<span><i>X<\/i><\/span>\u306e\u90e8\u5206\u306e\u90e8\u5206:<\/p><ul><li><span><a href=\"https:\/\/science-hub.click\/?p=54669\">\u7a7a\u96c6\u5408\u306f<\/a><\/span>\u6b21\u306e\u8981\u7d20\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\mathcal S} $$<\/div> ;<\/li><li>\u3059\u3079\u3066\u306e<span><i>A<\/i><\/span> \u3001 <span><i>B<\/i><\/span>\u8981\u7d20\u306b\u3064\u3044\u3066<div class=\"math-formual notranslate\">$$ {\\mathcal S} $$<\/div> \u3001\u30bb\u30c3\u30c8\u5dee<div class=\"math-formual notranslate\">$$ {A\\setminus B} $$<\/div>\u306e\u8981\u7d20\u306e\u7d20\uff08\u6709\u9650\uff09\u7d50\u5408\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal S} $$<\/div> ; <\/li><li><div class=\"math-formual notranslate\">$$ {\\mathcal S} $$<\/div>\u306f\uff08\u6709\u9650\uff09\u4ea4\u5dee\u306b\u3088\u3063\u3066\u5b89\u5b9a\u3057\u307e\u3059\u3002<\/li><\/ul><\/div><p>\u3055\u3089\u306b\u3001\u96c6\u5408<span><i>X \u304c<\/i><\/span>\u6b21\u306e\u8981\u7d20\u3067\u3042\u308b\u3068\u304d\u3001 <div class=\"math-formual notranslate\">$$ {\\mathcal S} $$<\/div> \u3001\u3068\u8a00\u308f\u308c\u3066\u3044\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal S} $$<\/div>\u306f<b>\u96c6\u5408\u306e\u534a\u4ee3\u6570<\/b>\u3067\u3059\u3002<\/p><h2>\u6e2c\u5b9a\u5024\u3092\u30bb\u30df\u30ea\u30f3\u30b0\u304b\u3089\u30ea\u30f3\u30b0\u306b\u62e1\u5f35\u3059\u308b<\/h2><p>\u534a\u30ea\u30f3\u30b0\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u308b\u30bb\u30c3\u30c8<span><a href=\"https:\/\/science-hub.click\/?p=81207\">\u306e\u30ea\u30f3\u30b0\u306f<\/a><\/span>\u7c21\u5358\u306b\u8aac\u660e\u3067\u304d\u307e\u3059\u3002<\/p><div><p><strong>\u547d\u984c<\/strong><span>\u2014<\/span>\u534a\u74b0\u3092\u542b\u3080\u96c6\u5408\u306e\u6700\u5c0f\u306e\u74b0<div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div>\u4e0e\u3048\u3089\u308c\u305f\u8981\u7d20\u306e\u6709\u9650\u7d50\u5408\u306e\u96c6\u5408\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3002\u305d\u308c\u306f\u307e\u305f\u3001\u6b21\u306e\u8981\u7d20\u306e\u6709\u9650\u306e\u7d20\u7d50\u5408\u306e\u30bb\u30c3\u30c8\u3067\u3082\u3042\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3002<\/p><\/div><p>\u7d9a\u304f\u62e1\u5f35\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u3067\u306f\u3001\u30af\u30e9\u30b9\u306e\u300c\u6e2c\u5b9a\u300d\u3092\u610f\u5473\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{C}} $$<\/div>\u7121\u52b9\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3092\u542b\u3080<div class=\"math-formual notranslate\">$$ {\\mathcal{C}} $$<\/div>\u306b\u5411\u304b\u3063\u3066<div class=\"math-formual notranslate\">$$ {[0,+\\infty]} $$<\/div>\u771f\u7a7a\u3068\u03c3\u52a0\u6cd5\u3067\u306f\u30bc\u30ed\u3002<\/p><div><p><strong>\u547d\u984c<\/strong><span>\u2014<\/span>\u3069\u3061\u3089\u304b<div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div>\u534a\u30ea\u30f3\u30b0\u3068<span>\u03bc<\/span>\u306e\u30e1\u30b8\u30e3\u30fc<div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3002\u3053\u306e\u5834\u5408\u3001 <span>\u03bc \u306f<\/span>1 \u3064\u306e\u62e1\u5f35\u3092\u8a31\u5bb9\u3057\u3001\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u305f\u96c6\u5408\u306e\u30ea\u30f3\u30b0\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u6e2c\u5ea6\u5185\u3067 1 \u3064\u306e\u307f\u3092\u8a31\u5bb9\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3002<\/p><\/div><p>\u6e2c\u5b9a\u5024\u306e\u76f8\u52a0\u6027\u3068\u3001\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u305f\u30ea\u30f3\u30b0\u306e\u8981\u7d20\u306e\u8aac\u660e\u3092\u8003\u616e\u3059\u308b\u3068\u3001\u305d\u306e\u72ec\u81ea\u6027\u306f\u660e\u3089\u304b\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> : \u3053\u306e\u30ea\u30f3\u30b0\u306e\u8981\u7d20<span><i>A<\/i><\/span>\u304c\u66f8\u304b\u308c\u3066\u3044\u308b\u5834\u5408\u306f\u5fc5\u305a<div class=\"math-formual notranslate\">$$ {A_1\\cup\\cdots\\cup A_n} $$<\/div>\u534a\u74b0\u306e<span><i>A<\/i> <sub><i>i<\/i><\/sub><\/span>\u8981\u7d20\u306e\u5834\u5408<div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3001\u79c1\u305f\u3061\u306f\u6301\u3063\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\mu(A)=\\mu(A_1)+\\cdots+ \\mu(A_n)} $$<\/div> \u3002\u5b58\u5728\u306b\u3064\u3044\u3066\u306f\u3001\u3053\u306e\u516c\u5f0f\u3092\u62e1\u5f35\u306e\u5b9a\u7fa9\u3068\u3057\u3066\u63a1\u7528\u3057\u307e\u3059\u3002\u6700\u521d\u306b\u3001\u305d\u308c\u304c\u4f7f\u7528\u3055\u308c\u308b<span><i>A<\/i><\/span>\u306e\u9664\u7b97\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3053\u3068\u3092\u78ba\u8a8d\u3057\u3066\u304b\u3089\u3001\u91cd\u5927\u306a\u969c\u5bb3\u306b\u906d\u9047\u3059\u308b\u3053\u3068\u306a\u304f\u30e1\u30b8\u30e3\u30fc\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p><p>\u534a\u74b0\u306e\u4ee3\u308f\u308a\u306b\u534a\u4ee3\u6570\u3092\u4f7f\u7528\u3057\u305f\u308a\u3001\u96c6\u5408\u74b0\u306e\u4ee3\u308f\u308a\u306b\u96c6\u5408\u4ee3\u6570\u3092\u4f7f\u7528\u3057\u305f\u985e\u4f3c\u306e\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u3082\u771f\u3067\u3042\u308a\u3001\u3053\u3053\u3067\u4e0e\u3048\u3089\u308c\u305f\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u304b\u3089\u3059\u3050\u306b\u63a8\u6e2c\u3055\u308c\u307e\u3059\u3002\u3069\u3061\u3089\u3092<span><a href=\"https:\/\/science-hub.click\/?p=61221\">\u4f7f\u7528\u3059\u308b<\/a><\/span>\u304b\u306f\u591a\u304f\u306e\u5834\u5408\u7121\u95a2\u5fc3\u3067\u3059\u3002\u534a\u4ee3\u6570\u306b\u53d6\u308a\u7d44\u3080\u3053\u3068\u306f\u3001\u03c3-\u4ee3\u6570\u306e\u6e2c\u5ea6\u3092\u69cb\u7bc9\u3059\u308b\u3068\u3044\u3046\u6700\u7d42\u76ee\u7684\u3068\u4e00\u81f4\u3057\u3066\u304a\u308a\u3001\u300c\u30ea\u30f3\u30b0\u300d\u3068\u3044\u3046\u8ffd\u52a0\u306e\u6982\u5ff5\u3092\u5c0e\u5165\u3059\u308b\u5fc5\u8981\u304c\u306a\u304f\u306a\u308a\u307e\u3059\u3002\u30bb\u30df\u30ea\u30f3\u30b0\u3092\u6271\u3046\u3053\u3068\u306b\u3088\u308a\u3001\u03c3-\u52a0\u6cd5\u6027\u306e\u521d\u671f\u691c\u8a3c\u3092\u7c21\u7d20\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u76ee\u7684\u304c \u03c3-\u30ea\u30f3\u30b0\u307e\u305f\u306f\u03b4-\u30ea\u30f3\u30b0\u3067\u306e\u6e2c\u5b9a\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u3067\u3042\u308b\u5834\u5408\u306b\u3082\u5341\u5206\u306b\u6b63\u5f53\u5316\u3055\u308c\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u96c6\u5408\u306e\u534a\u74b0 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/2L6JC2lWCfA\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u4f8b<\/h2><ul><li>\u3059\u3079\u3066\u306e\u9593\u9694<div class=\"math-formual notranslate\">$$ {\\R} $$<\/div>\u306f\u90e8\u5206\u306e\u534a\u4ee3\u6570\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\R} $$<\/div> (2 \u3064\u306e\u9593\u9694\u306e\u8a2d\u5b9a\u5dee\u306f\u3001\u305d\u308c\u3089\u306e\u76f8\u5bfe\u4f4d\u7f6e\u306b\u5fdc\u3058\u3066\u30010\u30011\u3001\u307e\u305f\u306f 2 \u3064\u306e\u9593\u9694\u306e\u7d20\u306e\u548c\u96c6\u5408\u3068\u3057\u3066\u8a18\u8ff0\u3067\u304d\u307e\u3059)\u3002<\/li><\/ul><ul><li>\u6709\u754c\u533a\u9593\u306e\u30bb\u30c3\u30c8<div class=\"math-formual notranslate\">$$ {\\R} $$<\/div>\u306f\u534a\u74b0\u3067\u3059\u304c\u534a\u4ee3\u6570\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/li><\/ul><ul><li>\u7a7a\u306e\u9593\u9694\u306e\u30bb\u30c3\u30c8\u3001\u307e\u305f\u306f<span>] <i>a<\/i> , <i>b<\/i> ]<\/span> ( <span><i>a<\/i> &lt; <i>b<\/i><\/span> ) \u306e\u5f62\u5f0f\u306e\u30bb\u30c3\u30c8\u306f\u3001\u524d\u306e\u9593\u9694\u306b\u542b\u307e\u308c\u308b\u534a\u30ea\u30f3\u30b0\u3067\u3059\u3002<\/li><\/ul><ul><li> 2 \u3064\u306e\u534a\u74b0\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408<div class=\"math-formual notranslate\">$$ {\\mathcal{S}_1} $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\mathcal{S}_2} $$<\/div>\u30bb\u30c3\u30c8<span><i>X<\/i> <sub>1<\/sub><\/span>\u304a\u3088\u3073<span><i>X<\/i> <sub>2<\/sub><\/span>\u306e\u3059\u3079\u3066\u306e\u7a4d<div class=\"math-formual notranslate\">$$ {A_1\\times A_2} $$<\/div> \u3001 <div class=\"math-formual notranslate\">$$ {A_i\\in \\mathcal{S}_i} $$<\/div>\u88fd\u54c1\u4e0a\u306e\u30bb\u30df\u30ea\u30f3\u30b0\u3067\u3059<div class=\"math-formual notranslate\">$$ {X_1\\times X_2.} $$<\/div> <span><i>X<\/i> <sub>1<\/sub><\/span>\u3068<span><i>X<\/i> <sub>2<\/sub><\/span>\u304c\u4ee3\u6570\u3067\u3042\u308b\u5834\u5408\u3067\u3082\u3001\u305d\u308c\u306f\u74b0\u3067\u306f\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059 (\u3082\u3061\u308d\u3093\u3001\u305d\u306e\u5834\u5408\u306f\u534a\u4ee3\u6570\u306b\u306a\u308a\u307e\u3059)\u3002\u3057\u305f\u304c\u3063\u3066\u3001 <span><i>n \u500b<\/i><\/span>\u306e\u6709\u754c\u533a\u9593\u306e\u7a4d\u306e\u96c6\u5408\u3001\u307e\u305f\u306f\u6b21\u306e\u5f62\u5f0f\u306e\u7a4d\u306e\u96c6\u5408<div class=\"math-formual notranslate\">$$ {]a_1,b_1]\\times\\cdots\\times]a_n,b_n]} $$<\/div>\u306e\u4e00\u90e8\u306e\u534a\u74b0\u3067\u3059\u304b\uff1f <div class=\"math-formual notranslate\">$$ {\\R^n} $$<\/div> \u3002<\/li><\/ul><h2>\u30bb\u30df\u30ea\u30f3\u30b0\u306e\u4f7f\u7528\u4f8b<\/h2><h3><span><span><i>n<\/i><\/span>\u6b21\u5143\u7a7a\u9593\u4e0a\u306e<span><a href=\"https:\/\/science-hub.click\/?p=96697\">\u30eb\u30d9\u30fc\u30b0\u6e2c\u5ea6<\/a><\/span>\u306e\u69cb\u7bc9<\/span><\/h3><p>\u30eb\u30d9\u30fc\u30b0\u6e2c\u5ea6\u3092\u69cb\u7bc9\u3059\u308b\u65b9\u6cd5\u306e 1 \u3064<div class=\"math-formual notranslate\">$$ {\\R^n} $$<\/div>\u3053\u308c\u306f\u3001\u7aef\u304c<span><i>a<\/i> <sub><i>i<\/i><\/sub><\/span>\u304a\u3088\u3073<span><i>b<\/i> <sub><i>i<\/i><\/sub><\/span>\u3067\u793a\u3055\u308c\u308b\u3001\u5883\u754c\u306e\u3042\u308b\u9593\u9694 (\u9589\u3058\u305f\u3001\u958b\u3044\u305f\u3001\u307e\u305f\u306f\u534a\u958b\u3044\u305f) \u306e\u76f4\u7dda\u30d6\u30ed\u30c3\u30af<span><i>P<\/i><\/span>\u306e\u7a4d\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u4f53\u7a4d\u306f\u5358\u306b\u8fba\u306e\u9577\u3055\u306e\u7a4d\u3067\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\mu(P)=\\prod_{i=1}^n(b_i-a_i).} $$<\/div><\/center><p>\u6b21\u306b\u3001\u3053\u306e\u5b9a\u7fa9\u3092\u30eb\u30d9\u30fc\u30b0\u53ef\u6e2c\u96c6\u5408\u306e\u30af\u30e9\u30b9\u306b\u62e1\u5f35\u3057\u307e\u3059\u3002<\/p><p>\u3053\u306e\u69cb\u7bc9\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=82055\">\u6700\u521d\u306b<\/a><\/span>\u6e2c\u5ea6\u3092\u6709\u754c\u533a\u9593\u306e\u3059\u3079\u3066\u306e\u548c\u96c6\u5408\u306e\u96c6\u5408\u306e\u30ea\u30f3\u30b0\u306b\u62e1\u5f35\u3059\u308b\u305f\u3081\u306b\u3001\u660e\u793a\u7684\u307e\u305f\u306f\u6697\u9ed9\u7684\u306b\u4e0a\u8a18\u306e\u547d\u984c\u3092\u547c\u3073\u51fa\u3059\u3053\u3068\u304b\u3089\u59cb\u307e\u308a\u307e\u3059\u3002\u534a\u74b0\u306e\u95a2\u5fc3\u306f\u3053\u3053\u3067\u660e\u3089\u304b\u306b\u73fe\u308c\u3066\u3044\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u62e1\u5f35\u306e\u6b21\u306e\u6bb5\u968e\u3067\u30ab\u30e9\u30c6\u30aa\u30c9\u30ea\u306e\u62e1\u5f35<span>\u5b9a\u7406<\/span>\u306b\u3088\u3063\u3066\u88dc\u8db3\u3055\u308c\u305f\u524d\u306e\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u306f\u3001\u6e2c\u5ea6\u306e \u03c3 \u52a0\u52a0\u6027\u304c<i>\u6700\u7d42\u7684\u306b\u306f<\/i>\u81ea\u5206\u81ea\u8eab\u3092\u5236\u9650\u3067\u304d\u308b \u03c3 \u52a0\u52a0\u6027\u30c1\u30a7\u30c3\u30af\u304b\u3089\u5f97\u3089\u308c\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u304b\u3089\u3067\u3059\u3002\u30bf\u30a4\u30eb\u306e\u64cd\u4f5c\u306b\u3002<\/p><p>\u4ee5\u4e0b\u306e\u30c9\u30ed\u30c3\u30d7\u30c0\u30a6\u30f3 \u30dc\u30c3\u30af\u30b9\u306b\u3053\u306e\u691c\u8a3c\u306e\u8a73\u7d30\u304c\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u7c21\u5358\u3067\u306f\u306a\u304f\u3001\u534a\u30ea\u30f3\u30b0\u306e\u64cd\u4f5c\u306e\u4f8b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/p><div align=\"left\"><div title=\"[\u62e1\u5927\u3059\u308b]\"><div align=\"left\"><p><br\/>\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046<div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div>\u6709\u754c\u533a\u9593\u7a4d\u306e\u534a\u30ea\u30f3\u30b0\u306f\u3001\u3053\u306e\u534a\u30ea\u30f3\u30b0\u4e0a\u306e\u30e1\u30b8\u30e3\u30fc\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p><p>\u307e\u305a\u3001 <span>\u03bc \u304c<\/span>\u6b21\u306e<span><a href=\"https:\/\/science-hub.click\/?p=81037\">\u610f\u5473<\/a><\/span>\u3067\u52a0\u6cd5\u7684\u3067\u3042\u308b<span><i>\u3053\u3068<\/i><\/span>\u3092\u793a\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> <span><i>P \u306f<\/i><\/span><span><a href=\"https:\/\/science-hub.click\/?p=13526\">\u6709\u9650\u65cf<\/a><\/span><span>( <i>Pi<\/i> <sub><i>)<\/i><\/sub><\/span>\u306e\u7d20\u548c\u96c6\u5408\u3067\u3042\u308a\u3001\u5404<span><i>P<\/i> <sub><i>i<\/i><\/sub><\/span>\u3082<div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3001\u5927\u304d\u306a\u30d6\u30ed\u30c3\u30af<span><i>P<\/i><\/span>\u306e\u4f53\u7a4d\u306f\u3001 <span><i>P<\/i> <sub><i>i<\/i><\/sub><\/span>\u306e\u4f53\u7a4d\u306e\u5408\u8a08\u3067\u3059\u3002<\/p><p>\u6b21\u306b\u3001 <span>\u03bc \u304c<\/span>\u5c3a\u5ea6\u3067\u3042\u308b\u3053\u3068\u3001\u3064\u307e\u308a \u03bc \u304c \u03c3 \u52a0\u6cd5\u7684\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3055\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u305d\u308c\u3092\u8a3c\u660e\u3059\u308b\u305f\u3081\u306b\u3001\u6b21\u306e\u30d6\u30ed\u30c3\u30af<span><i>P<\/i><\/span>\u8981\u7d20\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3001\u305d\u3057\u3066\u3001\u6b21\u306e\u30bf\u30a4\u30eb\u306e\u53ef\u7b97\u306a\u7d20\u7d50\u5408\u3068\u3057\u3066<span><i>P<\/i><\/span>\u306e\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u304c\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> : <\/p><center><div class=\"math-formual notranslate\">$$ {P=\\bigcup_{i=1}^{+\\infty}P_i} $$<\/div> \u3002<\/center><p>\u7b49\u3057\u3044\u3053\u3068\u3092\u793a\u3055\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093: <\/p><center><div class=\"math-formual notranslate\">$$ {\\mu(P)=\\sum_{i=1}^{+\\infty}\\mu(P_i)} $$<\/div> \u3002<\/center><p>\u3042\u308b\u610f\u5473\u3067\u306e\u4e0d\u5e73\u7b49\u306f\u3001\u7279\u306b\u72ec\u5275\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u3092\u5fc5\u8981\u3068\u3057\u307e\u305b\u3093\u3002\u56fa\u5b9a<span><i>r<\/i><\/span>\u306e\u5834\u5408\u3001\u305d\u306e\u5dee\u306f<div class=\"math-formual notranslate\">$$ {P\\setminus(P_1\\cup\\cdots\\cup P_r)} $$<\/div>\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u305f\u30ea\u30f3\u30b0\u5185\u306b\u3042\u308a\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001 \u306f\u8981\u7d20<span><i>F<\/i> <sub>1<\/sub><\/span> ,&#8230;, <span><i>F<\/i> <sub><i>s<\/i><\/sub><\/span>\u306e\u6709\u9650\u4e92\u3044\u306b\u7d20\u306a\u548c\u96c6\u5408\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d6\u30ed\u30c3\u30af<span><i>P \u306f<\/i><\/span>\u30011 \u304b\u3089<span><i>r<\/i><\/span>\u307e\u3067\u5909\u5316\u3059\u308b<span><i>i<\/i><\/span>\u306b\u5bfe\u3059\u308b\u3059\u3079\u3066\u306e<span><i>P<\/i> <sub><i>i \u3092<\/i><\/sub><\/span>\u542b\u3080\u30d6\u30ed\u30c3\u30af\u306e\u6709\u9650\u4e92\u3044\u306b\u7d20\u306a\u548c\u96c6\u5408\u3067\u3059\u3002 <span>\u03bc<\/span>\u306e\u6b63\u6027\u3068\u52a0\u6210\u6027\u306b\u3088\u308a\u3001\u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\sum_{i=1}^{r}\\mu(P_i)\\leq\\mu(P)} $$<\/div> \u3002<\/center><p> <span><i>r \u3092<\/i><\/span><span><a href=\"https:\/\/science-hub.click\/?p=96157\">\u7121\u9650\u5927<\/a><\/span>\u306b\u5411\u304b\u3046\u50be\u5411\u306b\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6b21\u306e\u7d50\u8ad6\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\sum_{i=1}^{+\\infty}\\mu(P_i)\\leq\\mu(P)} $$<\/div> \u3002<\/center><p><span><a href=\"https:\/\/science-hub.click\/?p=94311\">\u9006<\/a><\/span>\u4e0d\u7b49\u5f0f\u306f\u3001\u30eb\u30d9\u30fc\u30b0\u6e2c\u5ea6\u306e\u898f\u5247\u6027\u306b\u95a2\u3059\u308b\u4f4d\u76f8\u5e7e\u4f55\u5b66\u7684\u8003\u5bdf\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002\u307e\u305a\u3001 <span>\u03b5 &gt; 0<\/span>\u3092\u8a2d\u5b9a\u3057\u3001\u4f53\u7a4d\u304c<span>\u03bc( <i>Pi<\/i> <sub><i>)<\/i><\/sub> + \u03b5 \/ 2 <sup><i>i<\/i><\/sup><\/span>\u4ee5\u4e0b\u3067\u3042\u308b\u958b\u533a\u9593\u306e\u30bf\u30a4\u30eb<span><i>Q<\/i> <sub><i>i<\/i><\/sub><\/span>\u7a4d\u306b\u5404<span><i>P<\/i> <sub><i>i \u3092<\/i><\/sub><\/span>\u542b\u3081\u307e\u3059\u3002\u540c\u69d8\u306b\u3001 <span><i>P<\/i><\/span>\u306b\u542b\u307e\u308c\u3001\u305d\u306e\u4f53\u7a4d\u304c<span>\u03bc( <i>P<\/i> ) \u2212 \u03b5<\/span>\u4ee5\u4e0a\u3067\u3042\u308b\u9589\u533a\u9593\u306e\u30bf\u30a4\u30eb<span><i>Q<\/i><\/span>\u7a4d\u3092\u8003\u616e\u3057\u307e\u3059\u3002<\/p><p> Q \u30d1\u30c3\u30c9\u306f\u9589\u3058\u305f\u5883\u754c\u3068\u3057\u3066\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\R^n} $$<\/div>\u305d\u3057\u3066\u958b\u3044\u305f\u3082\u306e\u306f<span><i>Q<\/i><sub><i>\u79c1\u304c<\/i><\/sub><\/span>\u305d\u308c\u3092\u30ab\u30d0\u30fc\u3057\u307e\u3059\u3002\u30b5\u30d6\u30d5\u30a1\u30df\u30ea\u30fc\u3092\u62bd\u51fa\u3067\u304d\u307e\u3059<div class=\"math-formual notranslate\">$$ {(Q_{i})_{i\\in I_0}} $$<\/div>\u3053\u308c\u306f\u5e38\u306b\u305d\u308c\u3092\u30ab\u30d0\u30fc\u3057\u307e\u3059\u304c\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u6709\u9650\u30bb\u30c3\u30c8<span><i>I<\/i> <sub>0<\/sub><\/span>\u3067\u30ab\u30d0\u30fc\u3057\u307e\u3059\u3002<\/p><p>\u6709\u9650\u306e\u52a0\u6cd5\u6027\u3068\u534a\u74b0\u4e0a\u306e<span>\u03bc<\/span>\u306e\u6b63\u6027\u306b\u3088\u308b<div class=\"math-formual notranslate\">$$ {\\mathcal{S}} $$<\/div> \u3001\u6b21\u306e\u96c6\u5408\u5305\u542b (\u7d50\u5408\u304c\u7d20\u3067\u3042\u308b\u7406\u7531\u304c\u306a\u304f\u3001\u534a\u74b0\u306e\u6709\u9650\u6570\u306e\u8981\u7d20\u306e\u307f\u304c\u4ecb\u5728\u3059\u308b): <\/p><center><div class=\"math-formual notranslate\">$$ {Q\\subset\\bigcup_{i\\in I_0}Q_i} $$<\/div><\/center><p>\u4e0d\u7b49\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\mu(Q)\\leq\\sum_{i\\in I_0}\\mu(Q_i)} $$<\/div><\/center><p>\u305d\u3057\u3066<i>\u8981\u70b9<\/i>: <\/p><center><div class=\"math-formual notranslate\">$$ {\\mu(Q)\\leq\\sum_{i=1}^{+\\infty}\\mu(Q_i)} $$<\/div><\/center><p>\u3053\u308c\u306f\u4e0d\u7b49\u5f0f\u306e<span><a href=\"https:\/\/science-hub.click\/?p=78679\">\u9023\u9396<\/a><\/span>\u306b\u7d44\u307f\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\mu(P)-\\epsilon\\leq\\mu(Q)\\leq\\sum_{i=1}^{+\\infty}\\mu(Q_i)\\leq\\sum_{i=1}^{+\\infty}(\\mu(P_i)+{\\epsilon\\over2^i})=\\sum_{i=1}^{+\\infty}\\mu(P_i)+\\epsilon.} $$<\/div><\/center><p>\u6b8b\u3063\u3066\u3044\u308b\u306e\u306f\u3001 <span>\u03b5 \u3092<\/span>0 \u306b\u5411\u304b\u3046\u50be\u5411\u306b\u3057\u3066\u7d50\u8ad6\u3092\u200b\u200b\u5c0e\u304f\u3053\u3068\u3060\u3051\u3067\u3059\u3002<\/p><\/div><\/div><\/div><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u96c6\u5408\u306e\u534a\u74b0 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/FlG0UZZnTTI\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3> <span>Stieltjes \u30d7\u30ed\u30bb\u30b9\u3092\u4f7f\u7528\u3057\u305f\u5b9f\u6570\u76f4\u7dda\u4e0a\u306e\u6e2c\u5b9a\u5024\u306e\u69cb\u7bc9<\/span><\/h3><p>\u5b9f\u6570\u76f4\u7dda\u4e0a\u306e\u5c40\u6240\u7684\u306b\u6709\u9650\u306a\u5c3a\u5ea6\u306f\u3001\u4e0a\u3067\u8aac\u660e\u3057\u305f\u30d7\u30ed\u30bb\u30b9\u3092\u4e00\u822c\u5316\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002\u7a7a\u306e\u9593\u9694\u306e\u534a\u30ea\u30f3\u30b0\u3001\u307e\u305f\u306f<span>] <i>a<\/i> , <i>b<\/i> ]<\/span> ( <span><i>a<\/i> &lt; <i>b<\/i><\/span> ) \u306e\u5f62\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u306e\u304c\u9069\u5207\u3067\u3059\u3002<\/p><p>\u5897\u52a0\u3059\u308b\u6a5f\u80fd\u306b\u3064\u3044\u3066\u306f\u3001 <div class=\"math-formual notranslate\">$$ {\\R} $$<\/div>\u306b\u5411\u304b\u3063\u3066<div class=\"math-formual notranslate\">$$ {\\R} $$<\/div><span title=\"\u53f3\u5074\u3078\u306e\u9023\u7d9a\u6027 (\u30da\u30fc\u30b8\u306f\u5b58\u5728\u3057\u307e\u305b\u3093)\">\u7d9a\u3051\u3066\u53f3\u306b\u9032\u307f<\/span>\u3001\u6b21\u306e\u3088\u3046\u306b\u8a2d\u5b9a\u3057\u3066\u3053\u306e\u534a\u30ea\u30f3\u30b0\u4e0a\u306b\u30e1\u30b8\u30e3\u30fc\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002<\/p><center> <span>\u03bc(] <i>a<\/i> , <i>b<\/i> ]) = <i>F<\/i> ( <i>b<\/i> ) \u2212 <i>F<\/i> ( <i>a<\/i> )\u3001<\/span><\/center><p>\u305d\u306e\u7bc4\u56f2\u3092<span><a href=\"https:\/\/science-hub.click\/?p=70881\">\u30dc\u30ec\u30ea\u30a2\u306e\u90e8\u65cf<\/a><\/span>\u306b\u307e\u3067\u62e1\u5f35\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u308b\u3002 <div class=\"math-formual notranslate\">$$ {\\R} $$<\/div> \u3002\u78ba\u7387\u6e2c\u5ea6\u306e\u7279\u5b9a\u306e\u5834\u5408\u3001 <span><i>F \u306f<\/i><\/span>\u6e2c\u5ea6\u306e<span><a href=\"https:\/\/science-hub.click\/?p=4348\">\u5206\u5e03\u95a2\u6570<\/a><\/span>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p><p>\u3053\u306e\u65b9\u6cd5\u306f\u3001\u4efb\u610f\u306e\u6709\u9650<span><a href=\"https:\/\/science-hub.click\/?p=84871\">\u6b21\u5143<\/a><\/span>\u306b\u4e00\u822c\u5316\u3057\u307e\u3059\u3002<\/p><\/div><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u96c6\u5408\u306e\u534a\u74b0 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/JtE1PUJAybY\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/als.wikipedia.org\/wiki\/Menge_(Mathematik)\">Menge (Mathematik) \u2013 al\u00e9manique<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/am.wikipedia.org\/wiki\/%E1%88%B5%E1%89%A5%E1%88%B5%E1%89%A5\">\u1235\u1265\u1235\u1265 \u2013 amharique<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D8%A9_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)\">\u0645\u062c\u0645\u0648\u0639\u0629 (\u0631\u064a\u0627\u0636\u064a\u0627\u062a) \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ast.wikipedia.org\/wiki\/Conxuntu\">Conxuntu \u2013 asturien<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/az.wikipedia.org\/wiki\/%C3%87oxluqlar\">\u00c7oxluqlar \u2013 azerba\u00efdjanais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ba.wikipedia.org\/wiki\/%D0%9A%D2%AF%D0%BC%D3%99%D0%BA%D0%BB%D0%B5%D0%BA\">\u041a\u04af\u043c\u04d9\u043a\u043b\u0435\u043a \u2013 bachkir<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u96c6\u5408\u306e\u534a\u74b0 &#8211; \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u3010\u96c6\u5408\u8ad6\u3011\u6fc3\u5ea6\u304c\u6210\u3059\u9806\u5e8f\u96c6\u5408\u3010\u9078\u629e\u516c\u7406\u3011\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Zy9nsLq8sEw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u30bb\u30c3\u30c8\u306e\u30bb\u30df\u30ea\u30f3\u30b0(\u901a\u5e38\u306fsemiring\u3068\u7701\u7565\u3055\u308c\u307e\u3059) \u306f\u3001\u30bb\u30c3\u30c8\u306e\u30ea\u30f3\u30b0\u3092\u7c21\u5358\u306b\u69cb\u7bc9\u3067\u304d\u308b\u30bb\u30c3\u30c8X\u306e\u90e8\u5206\u306e\u30af\u30e9\u30b9\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u53e4\u5178\u7684\u306a\u6e2c\u5b9a\u69cb\u9020\u3092\u958b\u59cb\u3059\u308b\u306e\u306b\u4fbf\u5229\u306a\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u3067\u3059\u3002 \u610f\u5473 \u5b9a\u7fa9\u2014\u96c6 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":20701,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/pyxw_RxHuhs\/0.jpg","fifu_image_alt":"\u96c6\u5408\u306e\u534a\u74b0 - \u5b9a\u7fa9","footnotes":""},"categories":[5],"tags":[14332,22433,22432,11,13,14,10,12,8,16,15,9],"class_list":["post-20700","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-ensembles","tag-semi-anneau","tag-semi-anneau-densembles","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-dossier","tag-definition","tag-sciences","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/20700"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=20700"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/20700\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/20701"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=20700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=20700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=20700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}