{"id":65943,"date":"2023-11-07T08:54:38","date_gmt":"2023-11-07T08:54:38","guid":{"rendered":"https:\/\/science-hub.click\/%E3%82%A8%E3%83%B3%E3%83%88%E3%83%AD%E3%83%94%E3%83%BC%E3%83%A1%E3%83%88%E3%83%AA%E3%83%83%E3%82%AF-%E5%AE%9A%E7%BE%A9\/"},"modified":"2023-11-07T08:54:38","modified_gmt":"2023-11-07T08:54:38","slug":"%E3%82%A8%E3%83%B3%E3%83%88%E3%83%AD%E3%83%94%E3%83%BC%E3%83%A1%E3%83%88%E3%83%AA%E3%83%83%E3%82%AF-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=65943","title":{"rendered":"\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \u30e1\u30c8\u30ea\u30c3\u30af &#8211; \u5b9a\u7fa9"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p>\u6570\u5b66\u3001\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306e\u7406\u8ad6\u306b\u304a\u3044\u3066\u3001<b>\u8a08\u91cf\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<\/b>\u3001\u307e\u305f\u306f<b>\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5 \u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<\/b>(\u82f1\u8a9e\u3067\u306f<b>\u6e2c\u91cf\u7406\u8ad6\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<\/b>\u3068\u3082\u547c\u3070\u308c\u307e\u3059) \u306f\u30011950 \u5e74\u4ee3\u534a\u3070\u9803\u306b\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5\u306b\u3088\u3063\u3066\u958b\u767a\u3055\u308c\u305f\u30c4\u30fc\u30eb\u3067\u3042\u308a\u3001\u300c<span><a href=\"https:\/\/science-hub.click\/?p=1544\">\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<\/a><\/span>\u300d\u3068\u3044\u3046\u78ba\u7387\u8ad6\u7684\u306a\u6982\u5ff5\u306b\u7531\u6765\u3057\u3066\u3044\u307e\u3059\u3002\u30b7\u30e3\u30ce\u30f3\u306e\u60c5\u5831<span><a href=\"https:\/\/science-hub.click\/?p=11998\">\u7406\u8ad6<\/a><\/span>\u3002\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=65943\">\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u8a08\u91cf\u3092<\/a><\/span>\u4f7f\u7528\u3057\u3066 2 \u3064\u306e\u529b\u5b66\u7cfb\u304c\u5171\u5f79\u3067\u306a\u3044\u304b\u3069\u3046\u304b\u3092\u793a\u3059\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3001\u6e2c\u5b9a\u3055\u308c\u308b\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306e\u57fa\u672c\u7684\u306a\u4e0d\u5909\u91cf\u3067\u3059\u3002\u3055\u3089\u306b\u3001\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u6e2c\u5b9a\u57fa\u6e96\u306b\u3088\u308a\u3001\u30ab\u30aa\u30b9\u306e\u5b9a\u6027\u7684\u306a<span><a href=\"https:\/\/science-hub.click\/?p=74671\">\u5b9a\u7fa9<\/a><\/span>\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u30ab\u30aa\u30b9\u5909\u63db\u306f\u3001\u30bc\u30ed\u4ee5\u5916\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306e\u5909\u63db\u3068<span><a href=\"https:\/\/science-hub.click\/?p=98747\">\u898b\u306a\u3059<\/a><\/span>\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \u30e1\u30c8\u30ea\u30c3\u30af - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/Neb-wL4jXII\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u6307\u6a19\u306e\u69cb\u7bc9<\/h2><p><span><a href=\"https:\/\/science-hub.click\/?p=95765\">\u307e\u305a\u3001<\/a><\/span>\u79c1\u305f\u3061\u304c\u7f6e\u304b\u308c\u3066\u3044\u308b<span><a href=\"https:\/\/science-hub.click\/?p=66499\">\u6570\u5b66\u7684<\/a><\/span>\u67a0\u7d44\u307f\u3092\u63d0\u793a\u3057\u307e\u3057\u3087\u3046\u3002 <div class=\"math-formual notranslate\">$$ {(X, \\mathfrak{M}, \\mu)} $$<\/div>\u306f\u78ba\u7387\u7a7a\u9593\u3067\u3042\u308a\u3001 <div class=\"math-formual notranslate\">$$ {f: X \\to X} $$<\/div>\u306f\u6e2c\u5b9a\u53ef\u80fd\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u3042\u308a\u3001<span><a href=\"https:\/\/science-hub.click\/?p=38384\">\u4f4d\u76f8\u7a7a\u9593<\/a><\/span><i>X<\/i>\u4e0a\u306e\u96e2\u6563\u6642\u9593\u306b\u304a\u3051\u308b\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306e\u9032\u5316\u306e\u6cd5\u5247\u3092\u8868\u3057\u307e\u3059\u3002 <i>f<\/i>\u306b\u6e2c\u5ea6\u3092\u7dad\u6301\u3059\u308b\u3088\u3046\u8ab2\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001 <div class=\"math-formual notranslate\">$$ {\\forall M \\in \\mathfrak{M}, \\mu(f^{-1}(M)) = \\mu(M)} $$<\/div> \u3002\u521d\u671f\u72b6\u614b<i>x<\/i>\u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u305d\u306e\u53cd\u5fa9\u30b7\u30fc\u30b1\u30f3\u30b9\u3092<i>f<\/i>\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {x, f(x), \\dots, f^n(x), \\dots} $$<\/div>\u5168\u4f53<div class=\"math-formual notranslate\">$$ {\\{f^n(x)\u00a0: n \\geq 0\\}} $$<\/div>\u30b7\u30b9\u30c6\u30e0\u304c\u901a\u904e\u3059\u308b\u72b6\u614b\u306f<i>x<\/i>\u306e\u8ecc\u9053\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p><p>\u53ef\u6e2c\u96c6\u5408\u3067\u69cb\u6210\u3055\u308c\u308b<i>X<\/i>\u306e\u6709\u9650\u5206\u5272 \u03b1 \u3092\u4e0e\u3048\u308b\u3068\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\alpha = \\{A_1, \\dots, A_p\\}} $$<\/div>\u521d\u671f\u72b6\u614b<i>x<\/i> \u3001\u72b6\u614b<span><i>f<\/i> <sup><i>n<\/i><\/sup> ( <i>x<\/i> )<\/span> ( <div class=\"math-formual notranslate\">$$ {n \\geq 0} $$<\/div>\u30b7\u30b9\u30c6\u30e0\u304c\u901a\u904e\u3059\u308b ) \u306f\u305d\u308c\u305e\u308c\u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3 \u03b1 \u306e\u90e8\u5206\u306e 1 \u3064\u306b\u5206\u985e\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6b8b\u308a\u306e\u90e8\u5206\u306f\u3001\u521d\u671f\u72b6\u614b<i>x<\/i>\u306b\u95a2\u3059\u308b\u60c5\u5831\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f\u3001\u53cd\u5fa9\u306b\u3088\u3063\u3066\u63d0\u4f9b\u3055\u308c\u308b\u60c5\u5831\u306e<span><a href=\"https:\/\/science-hub.click\/?p=87799\">\u5e73\u5747<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=3678\">\u91cf<\/a><\/span>\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \u30e1\u30c8\u30ea\u30c3\u30af\u306e\u69cb\u7bc9\u306f\u3001\u4ee5\u4e0b\u3067\u8aac\u660e\u3059\u308b 3 \u3064\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u884c\u308f\u308c\u308b\u30d7\u30ed\u30bb\u30b9\u3067\u3059\u3002\u307e\u305a\u3001\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u5b9a\u7fa9\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\mathcal{H}(\\alpha)} $$<\/div>\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3 \u03b1 ( <i>x<\/i>\u306e\u70b9\u304c\u4f4d\u7f6e\u3059\u308b \u03b1 \u306e\u90e8\u5206\u306e\u77e5\u8b58\u304b\u3089\u5f97\u3089\u308c\u308b\u5e73\u5747\u60c5\u5831)\u3002\u6b21\u306b\u3001\u5206\u5272 \u03b1 (\u53cd\u5fa9\u306b\u3088\u3063\u3066\u63d0\u4f9b\u3055\u308c\u308b\u5e73\u5747\u60c5\u5831) \u306b\u5bfe\u3059\u308b\u5909\u63db<i>f<\/i>\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<span><i>h<\/i> ( <i>f<\/i> , \u03b1)<\/span>\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \u30e1\u30c8\u30ea\u30c3\u30af<i>h(f) \u306f<\/i>\u3001 <i>X<\/i>\u306e\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306b\u5bfe\u3059\u308b<i>f<\/i>\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306e\u4e0a\u9650\u3067\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \u30e1\u30c8\u30ea\u30c3\u30af - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/gUdHEZGwsuw\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<\/span><\/h3><p>\u03b1 \u3092\u53ef\u6e2c\u96c6\u5408\u3078\u306e<i>X<\/i>\u306e\u6709\u9650\u5206\u5272\u3068\u3059\u308b\u3002\u30ef\u30f3\u30dd\u30a4\u30f3\u30c8<div class=\"math-formual notranslate\">$$ {x \\in X} $$<\/div>\u4e00\u90e8\u306b\u4f4d\u7f6e\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u3055\u3089\u306b\u7acb\u5730\u304c\u826f\u3044\u3067\u3059<div class=\"math-formual notranslate\">$$ {A \\in \\alpha} $$<\/div>\u4f4e\u3044\u6e2c\u5b9a\u5024<span>\u03bc( <i>A<\/i> )<\/span> \u3002\u3053\u308c\u306f\u60c5\u5831\u6a5f\u80fd\u306e\u5c0e\u5165\u3092\u6b63\u5f53\u5316\u3059\u308b<div class=\"math-formual notranslate\">$$ {I(\\alpha)\u00a0: X \\to [0\u00a0; + \\infty ]} $$<\/div>\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059: <\/p><dl><dd><dl><dd><div class=\"math-formual notranslate\">$$ {\\forall x \\in X,  I(\\alpha)(x) = -\\sum_{A \\in \\alpha} \\log \\mu(A) \\chi_A(x)} $$<\/div><\/dd><\/dl><\/dd><\/dl><p>\u3064\u307e\u308a\u3001 <span><i>I<\/i> (\u03b1)( <i>x<\/i> ) = \u2212 log\u03bc( <i>A<\/i> )<\/span>\u306e\u5834\u5408<div class=\"math-formual notranslate\">$$ {x \\in A} $$<\/div> \u3002<\/p><p>\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3 \u03b1 \u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f<span><i>I<\/i> (\u03b1)<\/span>\u306e\u5e73\u5747\u3067\u3059\u3002 <\/p><dl><dd><dl><dd><div class=\"math-formual notranslate\">$$ {\\mathcal{H}(\\alpha) = \\frac{1}{\\mu(X)} \\int_X I(\\alpha)(x) d\\mu(x) = &#8211; \\sum_{A \\in \\alpha} \\mu(A) \\log \\mu(A)} $$<\/div><\/dd><\/dl><\/dd><\/dl><p> <span>0log0 \u3092<\/span>0 \u306b\u7b49\u3057\u3044\u3068\u3057\u307e\u3059\u3002 \u03b1 \u3068 \u03b2 \u304c<i>X<\/i>\u306e 2 \u3064\u306e\u6e2c\u5b9a\u53ef\u80fd\u306a\u5206\u5272\u3067\u3042\u308b\u5834\u5408\u3001\u03b1 \u3068 \u03b2 \u306e\u7d50\u5408\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\alpha \\vee \\beta} $$<\/div> \u03b1 \u3068 \u03b2 \u3088\u308a\u3082\u7d30\u304b\u3044\u6700\u5c0f\u306e\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3: <div class=\"math-formual notranslate\">$$ {\\alpha \\vee \\beta = \\{ A \\cap B\u00a0: A \\in \\alpha, B \\in \\beta, A \\cap B \\neq \\emptyset\\}} $$<\/div> \u3002 \u03b2 \u306f \u03b1 \u3088\u308a\u3082\u7d30\u304b\u3044\u3068\u8a00\u3044\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\beta \\geq \\alpha} $$<\/div> \u03b1 \u306e<i>A<\/i>\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u304c \u03b2 \u306e\u8981\u7d20\u306e\u548c\u96c6\u5408\u3068\u3057\u3066\u66f8\u304b\u308c\u305f\u5834\u5408\u3002<\/p><p>\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f\u3001\u6b21\u306e\u76f4\u611f\u7684\u306a\u7279\u6027\u3092\u6e80\u305f\u3057\u307e\u3059\u3002<\/p><ul><li> \u03b1 \u3068 \u03b2 \u304c 2 \u3064\u306e\u6e2c\u5b9a\u53ef\u80fd\u306a\u5206\u5272\u3067\u3042\u308b\u5834\u5408\u3001 <div class=\"math-formual notranslate\">$$ {\\mathcal{H}(\\alpha \\vee \\beta) \\leq \\mathcal{H}(\\alpha) + \\mathcal{H}(\\beta)} $$<\/div> \u3002<\/li><li>\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046<div class=\"math-formual notranslate\">$$ {f^{-1}(\\alpha) = \\{f^{-1}(A)\u00a0: A \\in \\alpha\\}} $$<\/div> \u3002\u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059\uff1a <div class=\"math-formual notranslate\">$$ {\\mathcal{H}(\\alpha) = \\mathcal{H}(f^{-1}(\\alpha))} $$<\/div> \u3002<\/li><\/ul><p>\u6700\u521d\u306e\u7279\u6027\u306f\u30012 \u3064\u306e\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306b\u5bfe\u3059\u308b\u30b7\u30b9\u30c6\u30e0\u306e\u72b6\u614b\u306e\u4f4d\u7f6e\u306e\u540c\u6642\u77e5\u8b58\u306b\u3088\u3063\u3066\u63d0\u4f9b\u3055\u308c\u308b\u60c5\u5831\u304c\u3001\u5404\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306b\u5bfe\u3057\u3066\u63d0\u4f9b\u3055\u308c\u308b\u60c5\u5831\u306e\u5408\u8a08\u3088\u308a\u3082\u5c11\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 2 \u756a\u76ee\u306e\u7279\u6027\u306f\u3001 <i>f \u304c<\/i>\u30e1\u30b8\u30e3\u30fc\u3092\u4fdd\u5b58\u3059\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u304b\u3089\u6765\u3066\u3044\u307e\u3059\u3002<\/p><h3><span>\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306b\u5bfe\u3059\u308b\u5909\u63db\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<\/span><\/h3><p>\u03b1 \u306f\u53ef\u6e2c\u5206\u5272\u3067\u3059\u3002 \u03b1 \u306b\u5bfe\u3059\u308b\u5909\u63db<i>f<\/i>\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<span><i>h<\/i> ( <i>f<\/i> ,\u03b1) \u3092<\/span>\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002 <\/p><dl><dd><dl><dd><div class=\"math-formual notranslate\">$$ {h(f, \\alpha) = \\lim_{n \\to + \\infty} \\frac{1}{n} \\mathcal{H} \\Bigg(\\bigvee_{i=0}^{n-1} f^{-i}(\\alpha) \\Bigg)} $$<\/div><\/dd><\/dl><\/dd><\/dl><p>\u5909\u63db<i>f<\/i>\u306f\u3001\u5b9f\u9a13\u4e2d\u306e\u3042\u308b<span><a href=\"https:\/\/science-hub.click\/?p=91861\">\u65e5<\/a><\/span>\u304b\u3089\u6b21\u306e\u65e5\u3078\u306e\u79fb\u884c\u3068\u3057\u3066\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6642\u9593<span><a href=\"https:\/\/science-hub.click\/?p=5522\">0<\/a><\/span>\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u72b6\u614b\u3092\u533a\u5225\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u533a\u5225\u3067\u304d\u306a\u3044\u72b6\u614b\u3092\u30d1\u30b1\u30c3\u30c8\u306b\u30b0\u30eb\u30fc\u30d7\u5316\u3057\u3001\u3053\u306e\u65b9\u6cd5\u3067\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3 \u03b1 \u3092\u5f62\u6210\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\bigvee_{i=0}^{n-1} f^{-i}(\\alpha)} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001 <i>n<\/i>\u65e5\u5f8c\u306e\u3059\u3079\u3066\u306e\u8003\u3048\u3089\u308c\u308b\u7d50\u679c\u3092\u8868\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001 <span><i>h<\/i> ( <i>f<\/i> , \u03b1) \u306f<\/span>\u3001\u5b9f\u9a13\u306e\u5b9f\u884c\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u5e73\u5747\u7684\u306a 1 \u65e5\u306e\u60c5\u5831\u3067\u3059\u3002<\/p><p>\u5b9a\u7fa9\u3055\u308c\u305f\u5236\u9650\u306f\u5b58\u5728\u3057\u307e\u3059\u3002\u6ce8\u610f\u3059\u308c\u3070<div class=\"math-formual notranslate\">$$ {a_n = \\mathcal{H} \\Bigg( \\bigvee_{i=0}^{n-1} f^{-i}(\\alpha) \\Bigg)} $$<\/div> \u3001\u6b8b\u308a\u306f<div class=\"math-formual notranslate\">$$ {(a_n)_{n \\in \\N^*}} $$<\/div>\u306f\u6e96\u52a0\u6cd5\u7684\u3067\u3042\u308b\u7406\u7531\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p><dl><dd><dl><dd><div class=\"math-formual notranslate\">$$ {a_{n+p} = \\mathcal{H} \\Bigg(\\bigvee_{i=0}^{n+p-1} f^{-i}(\\alpha) \\Bigg) \\leq \\mathcal{H} \\Bigg(\\bigvee_{i=0}^{n-1} f^{-i}(\\alpha) \\Bigg) + \\mathcal{H} \\Bigg(\\bigvee_{i=n}^{n+p-1} f^{-i}(\\alpha) \\Bigg) \\leq a_n + a_p} $$<\/div><\/dd><\/dl><\/dd><\/dl><p>\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e 2 \u3064\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u305d\u308c\u305e\u308c\u4f7f\u7528\u3057\u307e\u3057\u305f\u3002 <div class=\"math-formual notranslate\">$$ {(a_n\/n)_{n \\in \\N^*}} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001\u9650\u754c\u3092\u8a8d\u3081\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \u30e1\u30c8\u30ea\u30c3\u30af - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/EuWo5DzH3Cs\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u6700\u5f8c\u306e\u30b9\u30c6\u30c3\u30d7: \u5909\u63db\u306e\u30e1\u30c8\u30ea\u30c3\u30af \u30a8\u30f3\u30c8\u30ed\u30d4\u30fc<\/span><\/h3><p><i>h(f)<\/i>\u3067\u793a\u3055\u308c\u308b<i>f<\/i>\u306e\u8a08\u91cf\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f\u3001\u6709\u9650\u306e\u53ef\u6e2c\u5206\u5272\u306b\u5bfe\u3059\u308b<i>f<\/i>\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306e\u4e0a\u9650\u3067\u3059<i>\u3002<\/i> <\/p><dl><dd><dl><dd><div class=\"math-formual notranslate\">$$ {h(f) = \\sup_{\\alpha} h(f, \\alpha)} $$<\/div><\/dd><\/dl><\/dd><\/dl><p> <i>h(f) \u306f<\/i>\u304a\u305d\u3089\u304f\u7121\u9650\u5927\u3067\u3059\u3002<\/p><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Measure-theoretic_entropy\">Measure-theoretic entropy \u2013 anglais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/af.wikipedia.org\/wiki\/Entropie_(dubbelsinnig)\">Entropie (dubbelsinnig) \u2013 afrikaans<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D8%A5%D9%86%D8%AA%D8%B1%D9%88%D8%A8%D9%8A%D8%A7_(%D8%AA%D9%88%D8%B6%D9%8A%D8%AD)\">\u0625\u0646\u062a\u0631\u0648\u0628\u064a\u0627 (\u062a\u0648\u0636\u064a\u062d) \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/bar.wikipedia.org\/wiki\/Entropie\">Entropie \u2013 bavarois<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/be.wikipedia.org\/wiki\/%D0%AD%D0%BD%D1%82%D1%80%D0%B0%D0%BF%D1%96%D1%8F_(%D0%BD%D0%B5%D0%B0%D0%B4%D0%BD%D0%B0%D0%B7%D0%BD%D0%B0%D1%87%D0%BD%D0%B0%D1%81%D1%86%D1%8C)\">\u042d\u043d\u0442\u0440\u0430\u043f\u0456\u044f (\u043d\u0435\u0430\u0434\u043d\u0430\u0437\u043d\u0430\u0447\u043d\u0430\u0441\u0446\u044c) \u2013 bi\u00e9lorusse<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/be-tarask.wikipedia.org\/wiki\/%D0%AD%D0%BD%D1%82%D1%80%D0%B0%D0%BF%D1%96%D1%8F_(%D0%BD%D0%B5%D0%B0%D0%B4%D0%BD%D0%B0%D0%B7%D0%BD%D0%B0%D1%87%D0%BD%D0%B0%D1%81%D1%8C%D1%86%D1%8C)\">\u042d\u043d\u0442\u0440\u0430\u043f\u0456\u044f (\u043d\u0435\u0430\u0434\u043d\u0430\u0437\u043d\u0430\u0447\u043d\u0430\u0441\u044c\u0446\u044c) \u2013 Belarusian (Tara\u0161kievica orthography)<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \u30e1\u30c8\u30ea\u30c3\u30af &#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\u5927\u5b66\u7269\u7406\u3011\u71b1\u529b\u5b66\u5165\u9580\u2463(\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/gUdHEZGwsuw?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 \u6570\u5b66\u3001\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306e\u7406\u8ad6\u306b\u304a\u3044\u3066\u3001\u8a08\u91cf\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3001\u307e\u305f\u306f\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5 \u30a8\u30f3\u30c8\u30ed\u30d4\u30fc(\u82f1\u8a9e\u3067\u306f\u6e2c\u91cf\u7406\u8ad6\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3068\u3082\u547c\u3070\u308c\u307e\u3059) \u306f\u30011950 \u5e74\u4ee3\u534a\u3070\u9803\u306b\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5\u306b\u3088\u3063\u3066\u958b\u767a\u3055\u308c\u305f\u30c4\u30fc\u30eb\u3067\u3042\u308a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":65944,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/dyQ9VrBsXXg\/0.jpg","fifu_image_alt":"\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \u30e1\u30c8\u30ea\u30c3\u30af - \u5b9a\u7fa9","footnotes":""},"categories":[5],"tags":[1831,61606,11,13,10,14,13336,12,8,16,15,9],"class_list":["post-65943","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-entropie","tag-colorpoint","tag-techniques","tag-technologie","tag-actualite","tag-news","tag-metrique","tag-dossier","tag-definition","tag-sciences","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/65943"}],"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=65943"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/65943\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/65944"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=65943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=65943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=65943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}