{"id":99363,"date":"2023-10-30T23:54:24","date_gmt":"2023-10-30T23:54:24","guid":{"rendered":"https:\/\/science-hub.click\/%E8%BF%91%E6%89%80%28%E6%95%B0%E5%AD%A6%29-%E5%AE%9A%E7%BE%A9\/"},"modified":"2023-10-30T23:54:24","modified_gmt":"2023-10-30T23:54:24","slug":"%E8%BF%91%E6%89%80%28%E6%95%B0%E5%AD%A6%29-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=99363","title":{"rendered":"\u8fd1\u6240 (\u6570\u5b66) – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>

\u6570\u5b66\u3067\u306f\u3001\u8fd1\u508d<\/b>\u306e\u6982\u5ff5\u306f\u30c8\u30dd\u30ed\u30b8\u30fc\u306e\u6982\u5ff5\u3068\u540c\u7b49\u306e\u516c\u7406\u7684\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u30c8\u30dd\u30ed\u30b8\u306f\u3001\u9023\u7d9a\u6027\u306a\u3069\u306e\u30b0\u30ed\u30fc\u30d0\u30eb\u306a\u6982\u5ff5\u3092\u3088\u308a\u81ea\u7136\u306b\u6271\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u3059\u3079\u3066\u306e<\/a><\/span>\u70b9<\/a><\/span>\u3067\u306e\u9023\u7d9a\u6027<\/a><\/span>\u3068\u3057\u3066\u7406\u89e3\u3055\u308c\u307e\u3059\u3002\u4e00\u65b9\u3001\u70b9\u3084\u6975\u9650\u3067\u306e\u9023\u7d9a\u6027\u306a\u3069\u306e\u5c40\u6240\u7684\u306a\u30d7\u30ed\u30d1\u30c6\u30a3\u306e\u5834\u5408\u3001\u8fd1\u508d\u5f62\u5f0f\u306e\u65b9\u304c\u5358\u7d14\u3067\u3042\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002<\/p>

\n\"\u8fd1\u6240<\/figure>

\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7a7a\u9593\u306b\u304a\u3051\u308b\u8fd1\u508d<\/h2>

\u4f4d\u76f8\u7a7a\u9593\u3067\u306f\u3001\u70b9\u306e\u8fd1\u508d\u306f\u3001<\/b>\u3053\u306e\u70b9\u3092\u542b\u3080\u958b\u3044\u305f\u90e8\u5206\u3092\u542b\u3080\u30b5\u30d6\u30bb\u30c3\u30c8<\/a><\/span>\u3067\u3059\u3002\u3069\u3061\u3089\u304b

$$ {E\\;} $$<\/div>\u4f4d\u76f8\u7a7a\u9593\u3068
$$ {a\\;} $$<\/div>\u306e\u30dd\u30a4\u30f3\u30c8
$$ {E\\;} $$<\/div> \u3002\u305d\u308c\u3067\u306f\u6ce8\u610f\u3057\u3066\u307f\u307e\u3057\u3087\u3046
$$ {\\mathcal V(a)} $$<\/div>\u3059\u3079\u3066\u306e\u8fd1\u6240
$$ {a\\;} $$<\/div> \u3002\u3059\u308b\u3068\u6b21\u306e\u3053\u3068\u306b\u6c17\u3065\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>
  1. $$ {E\\in \\mathcal V(a)} $$<\/div> \uff08\u305d\u308c\u3067
    $$ {\\mathcal V(a)\\ne\\varnothing } $$<\/div> ) <\/li>
  2. $$ {A,B\\in \\mathcal V(a) ~\\Rightarrow~ A\\cap B\\in \\mathcal V(a)} $$<\/div><\/li>
  3. $$ {A\\in \\mathcal V(a) ~\\land~ A\\subset B\\subset E ~\\Rightarrow~ B\\in \\mathcal V(a)} $$<\/div><\/li>
  4. $$ {\\varnothing\\notin \\mathcal V(a)} $$<\/div><\/li><\/ol>

    \u79c1\u305f\u3061\u306f\u3001\u6b21\u306e\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002

    $$ {a\\;} $$<\/div>\u306b\u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u5f62\u6210\u3059\u308b
    $$ {E\\;} $$<\/div>\u542b\u3081\u308b\u305f\u3081\u306b\u3002\u3055\u3089\u306b\u6b21\u306e\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059 (\u30aa\u30fc\u30d7\u30f3\u306f\u305d\u306e\u5404\u30dd\u30a4\u30f3\u30c8\u306e\u8fd1\u508d\u3067\u3042\u308b\u305f\u3081): <\/p>

    $$ {A \\in \\mathcal V(a)\\Rightarrow\\exist B \\subset A,\\quad a\\in B} $$<\/div>\u305d\u3057\u3066
    $$ {\\forall b\\in B, B\\in\\mathcal V(b) } $$<\/div><\/p>

    (\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059)

    $$ {A \\in \\mathcal V(a)\\Rightarrow a\\in A\\Rightarrow A\\neq\\varnothing} $$<\/div> )<\/p>

    \u8fd1\u96a3\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9<\/h2>

    \u70b9\u306e\u8fd1\u508d\u306e\u30bb\u30c3\u30c8\u306f\u5e83\u5927\u3067\u3059\u3002\u5305\u542b\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u5206\u6790\u306b\u3088\u308a\u3001\u3053\u306e\u8fd1\u508d\u30bb\u30c3\u30c8\u3092\u5b9a\u7fa9\u3059\u308b\u306b\u306f\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u57fa\u790e<\/b>\u306e\u307f\u3092\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u57fa\u672c\u6982\u5ff5\u304b\u3089\u76f4\u63a5\u63a8\u5b9a\u3055\u308c\u308b\u5b9a\u7fa9\u306f<\/a><\/span>\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 \u70b9\u306e\u8fd1\u508d\u306e\u57fa\u5e95<\/b>

    $$ {a\\;} $$<\/div>\u30bb\u30c3\u30c8\u306e
    $$ {E\\;} $$<\/div>\u7a7a\u3067\u306f\u306a\u3044\u5bb6\u65cf\u3067\u3059
    $$ {\\mathcal W(a)} $$<\/div>\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u306e
    $$ {E\\;} $$<\/div>\u3059\u3079\u3066\u3092\u542b\u3080
    $$ {a\\;} $$<\/div>\u305d\u3057\u3066\u3001\u6b21\u306e 2 \u3064\u306e\u8981\u7d20\u306e\u4ea4\u5dee\u304c\u6210\u7acb\u3059\u308b\u3088\u3046\u306b\u3001
    $$ {\\mathcal W(a)} $$<\/div>\u306e\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059
    $$ {\\mathcal W(a)} $$<\/div> \u3002<\/p>

    \u306e\u8fd1\u6240

    $$ {a\\;} $$<\/div>\u306e\u8981\u7d20\u3092\u542b\u3080 E \u306e\u4efb\u610f\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u306b\u306a\u308a\u307e\u3059\u3002
    $$ {\\mathcal W(a)} $$<\/div> \u3002<\/p>

    \u8fd1\u508d\u304b\u3089\u5b9a\u7fa9\u3055\u308c\u305f\u30c8\u30dd\u30ed\u30b8<\/h2>

    \u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u30c8\u30dd\u30ed\u30b8\u30fc\u306e\u516c\u7406\u304c\u5404\u70b9\u306e\u8fd1\u508d\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f\u3002\u6b21\u306b\u3001\u8fd1\u508d\u306e\u30bb\u30c3\u30c8\u3092\u516c\u7406\u7684\u306b\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5b9a\u7fa9\u306b\u3088\u308a\u3001\u30c8\u30dd\u30ed\u30b8\u3092\u5b9a\u7fa9\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

    \u3069\u3061\u3089\u304b

    $$ {E\\;} $$<\/div>\u30bb\u30c3\u30c8\u3002\u306e\u5fdc\u7528
    $$ {E\\;} $$<\/div>\u3067
    $$ {\\mathcal P(\\mathcal P(E))} $$<\/div>\u6ce8\u76ee\u3057\u305f
    $$ {\\mathcal V\\;} $$<\/div>\u6b21\u306e\u5834\u5408\u306b\u9650\u308a\u3001\u4e00\u9023\u306e\u8fd1\u508d\u3092\u5f62\u6210\u3057\u307e\u3059\u3002<\/p>
    1. \u30d5\u30a3\u30eb\u30bf\u304c\u30aa\u30f3\u306b\u306a\u3063\u3066\u3044\u307e\u3059
      $$ {E\\;} $$<\/div>\u542b\u3081\u308b\u305f\u3081\u306b<\/li>
    2. $$ {\\forall a\\in E\\quad\\forall A \\in \\mathcal V(a) \\quad\\exist B \\subset A,\\quad a\\in B} $$<\/div>\u305d\u3057\u3066
      $$ {\\forall b\\in B, B\\in\\mathcal V(b) } $$<\/div><\/li><\/ol>

      \u6b21\u306b\u3001\u6b21\u306e\u3059\u3079\u3066\u306e\u90e8\u5206\u3092\u691c\u8a0e\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002

      $$ {E\\;} $$<\/div>\u3053\u308c\u3089\u306f\u305d\u308c\u305e\u308c\u306e\u30dd\u30a4\u30f3\u30c8\u306e\u8fd1\u508d\u3067\u3059\u3002\u3053\u306e\u30bb\u30c3\u30c8\u304c\u30c8\u30dd\u30ed\u30b8\u3092\u5f62\u6210\u3057\u307e\u3059\u3002<\/p>
      \n\"\u8fd1\u6240<\/figure>

      \u4f8b<\/h2>

      \u6b63\u306e\u6574\u6570\u306e\u5834\u5408<\/span><\/h3>

      \u5b8c\u4e86\u3059\u308b\u3053\u3068\u306f\u53ef\u80fd\u3067\u3059

      $$ {\\N} $$<\/div>\u5024\u3068\u4e00\u7dd2\u306b
      $$ {+\\infty\\;} $$<\/div> \u3002\u3053\u306e\u7a7a\u9593\u306b\u3001\u5024\u3092\u542b\u3080\u6709\u9650\u96c6\u5408\u306e\u3059\u3079\u3066\u306e\u88dc\u6570\u3092\u542b\u3080\u30d5\u30ec\u30b7\u30a7 \u30d5\u30a3\u30eb\u30bf\u3092\u95a2\u9023\u4ed8\u3051\u308b\u5834\u5408\u3001
      $$ {+\\infty\\;} $$<\/div> \u3002\u305d\u308c\u3067
      $$ {+\\infty\\;} $$<\/div>\u306b\u306f\u4e00\u9023\u306e\u8fd1\u96a3\u5730\u57df\u304c\u3042\u308a\u307e\u3059\u3002\u6b21\u306b\u3001\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u5236\u9650\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002
      $$ {(u_n)\\;} $$<\/div>\u4fa1\u5024\u3092\u7f6e\u304f
      $$ {\\R} $$<\/div>\u307e\u305f\u306f
      $$ {\\mathbb C} $$<\/div> \u3002\u3053\u306e\u6570\u5217\u306f\u6b21\u306e\u5024\u306b\u53ce\u675f\u3057\u307e\u3059\u3002
      $$ {l\\;} $$<\/div>\u3044\u3064
      $$ {n\\;} $$<\/div>\u50be\u5411\u304c\u3042\u308b
      $$ {+\\infty\\;} $$<\/div>\u6b21\u306e\u5834\u5408\u306b\u306e\u307f: <\/p>
      $$ {\\forall \\epsilon > 0 \\quad \\exist N \\in \\mathbb N \\quad \\forall n > N \\quad |u_n- l|<\\epsilon \\;} $$<\/div><\/dl>

      \u5b9f\u6570\u306e\u5834\u5408<\/span><\/h3>

      \u5b9f\u6570\u306e\u30bb\u30c3\u30c8\u306b\u304a\u3044\u3066\u3001\u5b9f\u6570a<\/i>\u306e\u8fd1\u508d\u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002 <\/p>