[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13386#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13386","headline":"\u30b3\u30f3\u30c6\u30f3\u30c4\uff08\u6e2c\u5b9a\u7406\u8ad6\uff09 &#8211; \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u30b3\u30f3\u30c6\u30f3\u30c4\uff08\u6e2c\u5b9a\u7406\u8ad6\uff09 &#8211; \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"\u30b3\u30f3\u30c6\u30f3\u30c4\u306f\u3001\u5bf8\u6cd5\u306e\u7279\u5225\u306a\u6570\u91cf\u95a2\u6570\u3067\u3042\u308a\u3001\u7279\u5b9a\u306e\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306b\u5bfe\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3001\u4f53\u7a4d\u306e\u76f4\u611f\u7684\u306a\u6982\u5ff5\u3092\u62bd\u8c61\u5316\u3057\u3001\u4e00\u822c\u5316\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002 \u30b3\u30f3\u30c6\u30f3\u30c4\u306e\u6709\u9650\u6dfb\u52a0\u5264 m {displaystyle mu} \uff1a\u6700\u7d42\u7684\u306a\u9038\u8131\u5354\u4f1a\u306e\u5185\u5bb9\u306f\u3001\u500b\u3005\u306e\u30b5\u30d6\u91cf\u306e\u5185\u5bb9\u306e\u5408\u8a08\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002 \u4efb\u610f\u306e\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u3067 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u304c\u3042\u308a\u307e\u3059 c {displaystyle {mathcal {c}}} \u3001\u7a7a\u306e\u91cf\u3092\u542b\u3080\u3002\u6b21\u306b\u3001\u6570\u91cf\u95a2\u6570\u304c\u547c\u3073\u51fa\u3055\u308c\u307e\u3059 m \uff1a","datePublished":"2022-05-16","dateModified":"2022-05-16","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/3b\/Finite_additivity_of_measure.svg\/300px-Finite_additivity_of_measure.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/3b\/Finite_additivity_of_measure.svg\/300px-Finite_additivity_of_measure.svg.png","height":"81","width":"300"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13386","wordCount":10819,"articleBody":"\u30b3\u30f3\u30c6\u30f3\u30c4\u306f\u3001\u5bf8\u6cd5\u306e\u7279\u5225\u306a\u6570\u91cf\u95a2\u6570\u3067\u3042\u308a\u3001\u7279\u5b9a\u306e\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306b\u5bfe\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3001\u4f53\u7a4d\u306e\u76f4\u611f\u7684\u306a\u6982\u5ff5\u3092\u62bd\u8c61\u5316\u3057\u3001\u4e00\u822c\u5316\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002  \u30b3\u30f3\u30c6\u30f3\u30c4\u306e\u6709\u9650\u6dfb\u52a0\u5264 m {displaystyle mu} \uff1a\u6700\u7d42\u7684\u306a\u9038\u8131\u5354\u4f1a\u306e\u5185\u5bb9\u306f\u3001\u500b\u3005\u306e\u30b5\u30d6\u91cf\u306e\u5185\u5bb9\u306e\u5408\u8a08\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002 \u4efb\u610f\u306e\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u3067 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u304c\u3042\u308a\u307e\u3059 c {displaystyle {mathcal {c}}} \u3001\u7a7a\u306e\u91cf\u3092\u542b\u3080\u3002\u6b21\u306b\u3001\u6570\u91cf\u95a2\u6570\u304c\u547c\u3073\u51fa\u3055\u308c\u307e\u3059 m \uff1a C\u2192 [ 0 \u3001 \u221e ] {displaystyle mu\uff1a{mathcal {c}}\u304b\u3089[0\u3001infty]} a \u30b3\u30f3\u30c6\u30f3\u30c4 \u4ee5\u4e0b\u304c\u9069\u7528\u3055\u308c\u308b\u5834\u5408\uff1a [\u521d\u3081] \u7a7a\u306e\u91d1\u984d\u306b\u306f\u30bc\u30ed\u306e\u5024\u304c\u3042\u308a\u307e\u3059\u3002 m \uff08 \u2205 \uff09\uff09 = 0 {displaystyle mu\uff08emptySet\uff09= 0} \u3002 \u95a2\u6570\u306f\u3067\u3059 \u6700\u5f8c\u306b\u6dfb\u52a0\u5264 \u3002\u305d\u3046\u3067\u3059 a 1\u3001 a 2\u3001 &#8230; \u3001 a n{displaystyle a_ {1}\u3001a_ {2}\u3001dotsc\u3001a_ {n}} \u6700\u5f8c\u306b\u3001\u30da\u30a2\u306e\u591a\u304f\u306e\u5206\u96e2\u91cf\u304c\u51fa\u307e\u3059 C{displaystyle {mathcal {c}}} \u3068 \u22c3i=1nAi\u2208 C{displaystyle textStyle bigcup _ {i = 1}^{n} a_ {i} in {mathcal {c}}} \u6b21\u306b\u3001\u9069\u7528\u3057\u307e\u3059 \u03bc(\u22c3i=1nAi)=\u2211i=1n\u03bc(Ai){displaystyle mu left\uff08bigcup _ {i = 1}^{n} a_ {i} right\uff09= sum _ {i = 1}^{n} {mu\uff08a_ {i}\uff09}}} \u3002 \u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306f\u901a\u5e38\u3001\u6570\u91cf\u30c9\u30fc\u30e0\u3067\u3059\u3002 [2] [3] \u8ff0\u3079\u308b [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5b9a\u7fa9\u3067\u306f\u3001\u5206\u96e2\u578b\u306e\u6709\u9650\u306e\u95a2\u9023\u6027\u304c\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306b\u623b\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u5fc5\u8981\u3068\u3057\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u308c\u3060\u3051\u304c\u5fc5\u8981\u3067\u3059 \u6edd \u5206\u96e2\u5354\u4f1a\u306f\u518d\u3073\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306b\u3042\u308a\u3001\u6709\u9650\u6dfb\u52a0\u5264\u304c\u9069\u7528\u3055\u308c\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u5206\u96e2\u578b\u306e\u6709\u9650\u306e\u95a2\u9023\u6027\u306f\u3001\u4e00\u822c\u306b\u30cf\u30fc\u30d6\u30ea\u30f3\u30b0\u306b\u623b\u3063\u3066\u3044\u307e\u305b\u3093\u3002\u3053\u306e\u4f8b\u306f\u3001\u534a\u5206\u306e\u30ea\u30c3\u30b7\u30f3\u30b0\u3067\u3059 r {displaystyle mathbb {r}} \u30d5\u30a9\u30fc\u30e0\u306e\u30cf\u30fc\u30d5\u30aa\u30fc\u30d7\u30f3\u9593\u9694\u304b\u3089\u306e\u3082\u306e [ a \u3001 b \uff09\uff09 {displaystyle [a\u3001b\uff09} \u69cb\u6210\u3055\u308c\u307e\u3059\u3002 \u540c\u69d8\u306b\u3001\u4e00\u822c\u306b\u3001\u6dfb\u52a0\u5264\u304b\u3089\u3001\u3064\u307e\u308a\u30d7\u30ed\u30d1\u30c6\u30a3\u304b\u3089 m \uff08 a \u222a b \uff09\uff09 = m \uff08 a \uff09\uff09 + m \uff08 b \uff09\uff09 {displaystyle mu\uff08acup b\uff09= mu\uff08a\uff09+mu\uff08b\uff09} \u5206\u96e2\u6cd5\u306e\u305f\u3081\u306b a \u3001 b {displaystyle a\u3001b} \u3068 a \u222a b \u2208 c {displaystyle acup bin {mathcal {c}}} \u6709\u9650\u6dfb\u52a0\u5264\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u4e8b\u5b9f\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059 a \u222a b \u2208 c {displaystyle acup bin {mathcal {c}}} \u4e00\u822c\u7684\u306a\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u3067\u306f\u3042\u308a\u307e\u305b\u3093 a \u222a b \u222a c \u2208 c {displaysyle acup bcup cin {mathcal {c}}} \u5acc\u3044\u306e\u305f\u3081\u306b\u7d9a\u304d\u307e\u3059 c \u2208 c {displaystyle cin {mathcal {c}}} \u3002\u6dfb\u52a0\u5264\u304b\u3089\u6709\u9650\u6dfb\u52a0\u5264\u3078\u306e\uff08\u5f8c\u65b9\u306e\uff09\u5e30\u7d0d\u7684\u7d50\u8ad6\u306f\u3001\u7d71\u4e00\u5b89\u5b9a\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306b\u306e\u307f\u9069\u7528\u3055\u308c\u307e\u3059\u3002 \u7d71\u4e00\u3055\u308c\u305f\u5b89\u5b9a\u3057\u305f\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306b\u3064\u3044\u3066 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e0a\u8a18\u306e\u8003\u616e\u4e8b\u9805\u306b\u57fa\u3065\u3044\u3066\u3001\u7d71\u4e00\u5b89\u5b9a\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u3067\u6b21\u306e\u7c21\u7d20\u5316\u3055\u308c\u305f\u5b9a\u7fa9\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u306f \u306e {displaystyle {mathcal {v}}} \u7a7a\u306e\u6570\u91cf\u3092\u542b\u3080\u7d71\u4e00\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306f\u6570\u91cf\u95a2\u6570\u3067\u3059 m \uff1a V\u2192 [ 0 \u3001 \u221e ] {displaystyle mu\uff1a{mathcal {v}}\u304b\u3089[0\u3001infty]} a \u30b3\u30f3\u30c6\u30f3\u30c4 \u4ee5\u4e0b\u304c\u9069\u7528\u3055\u308c\u308b\u5834\u5408\uff1a \u7a7a\u306e\u91d1\u984d\u306b\u306f\u30bc\u30ed\u306e\u5024\u304c\u3042\u308a\u307e\u3059\u3002 m \uff08 \u2205 \uff09\uff09 = 0 {displaystyle mu\uff08emptySet\uff09= 0} \u3002 \u95a2\u6570\u306f\u3067\u3059 \u6dfb\u52a0\u5264 \u3001\u3064\u307e\u308a\u3001\u305d\u308c\u305e\u308c2\u3064\u306e\u5206\u96e2\u304c\u3042\u308a\u307e\u3059 a \u3001 b \u2208 V{displaystyle a\u3001bin {mathcal {v}}} \u9069\u7528\u53ef\u80fd\u3067\u3059 \u03bc(A\u222aB)=\u03bc(A)+\u03bc(B){displaystyle mu\uff08acup b\uff09= mu\uff08a\uff09+mu\uff08b\uff09} \u3002 \u7d71\u4e00\u5b89\u5b9a\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306f\u901a\u5e38\u3001\u6570\u91cf\u30ea\u30f3\u30b0\u3067\u3059\u3002 \u6700\u3082\u91cd\u8981\u306a\u30b3\u30f3\u30c6\u30f3\u30c4\u306f\u3001SO -CALLED LEESGUE\u30b3\u30f3\u30c6\u30f3\u30c4\u3067\u3059 m \uff08 [ a \u3001 b \uff09\uff09 \uff09\uff09 = b  &#8211;  a {displaystyle mu\uff08[a\u3001b\uff09\uff09= b-a} \u3002 \u534a\u5206\u306e\u9593\u9694\u3067 [ a \u3001 b \uff09\uff09 {displaystyle [a\u3001b\uff09} \u5b9f\u6570\u306b\u3064\u3044\u3066\u3002\u6700\u7d42\u7684\u306b\u62e1\u5f35\u3068\u3055\u307e\u3056\u307e\u306a\u7d99\u7d9a\u7387\u3092\u901a\u3058\u3066\u69cb\u7bc9\u3055\u308c\u307e\u3059\u3002\u5b9f\u969b\u3001\u3053\u306e\u30b3\u30f3\u30c6\u30f3\u30c4\u306f\u3059\u3067\u306b\u6b21\u5143\u4ee5\u524d\u306e\u30b3\u30f3\u30c6\u30f3\u30c4\u3067\u3059\u3002 \u3082\u30461\u3064\u306e\u91cd\u8981\u306a\u30b3\u30f3\u30c6\u30f3\u30c4\u306f\u3001Lebesgue-stalulajes\u304c\u6e2c\u5b9a\u3059\u308bSteltjes\u306e\u30b3\u30f3\u30c6\u30f3\u30c4\u3068\u3001Lebesgue-Stales-Integreal\u304c\u5c0e\u51fa\u3055\u308c\u308b\u3053\u3068\u3067\u3059\u3002 m F\uff08 [ a \u3001 b \uff09\uff09 \uff09\uff09 = f \uff08 b \uff09\uff09  &#8211;  f \uff08 a \uff09\uff09 {displaystyle mu _ {f}\uff08[a\u3001b\uff09\uff09= f\uff08b\uff09-f\uff08a\uff09} \u3001 \u3057\u305f\u304c\u3063\u3066 f {displaystyle f} \u5358\u8abf\u306a\u672c\u5f53\u306e\u6a5f\u80fd\u3002\u5b9f\u6570\u306e\u3059\u3079\u3066\u306e\u6709\u9650\u30b3\u30f3\u30c6\u30f3\u30c4\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 \u5225\u306e\u30b3\u30f3\u30c6\u30f3\u30c4\u306f\u30e8\u30eb\u30c0\u30f3\u306e\u5c3a\u5ea6\u3067\u3059\u3002\u540d\u524d\u306b\u53cd\u3057\u3066\u3001\u305d\u308c\u306f\u6e2c\u5b9a\u7406\u8ad6\u306e\u89b3\u70b9\u304b\u3089\u306e\u5c3a\u5ea6\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u306b\u5fdc\u3058\u3066\u3001\u7279\u5b9a\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u304c\u9069\u7528\u3055\u308c\u307e\u3059\u3002 \u30cf\u30eb\u30d6\u30ea\u30f3\u30b0\u3067 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6edd c = h {displaystyle {mathcal {c}} = {mathcal {h}}}} \u305d\u306e\u5f8c\u3001\u534a\u8d70\u884c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u3059\u3079\u3066\u306e\u30b3\u30f3\u30c6\u30f3\u30c4 m {displaystyle mu} \u306f \u5358\u8abf\u306a \u3001\u3057\u305f\u304c\u3063\u3066\u3001\u305d\u308c\u306f\u771f\u5b9f\u3067\u3059\uff1a a \u2286 b \u21d2 m \uff08 a \uff09\uff09 \u2264 m \uff08 b \uff09\uff09 {displaystyle asubseteq brightarrow mu\uff08a\uff09leq mu\uff08b\uff09} \u305f\u3081\u306b a \u3001 b \u2208 H{displaystyle a\u3001bin {mathcal {h}}} \u3002 \u3059\u3079\u3066\u306e\u30b3\u30f3\u30c6\u30f3\u30c4 m {displaystyle mu} \u306f subadditiv \u3057\u305f\u304c\u3063\u3066\u3001\u305d\u308c\u306f\u9069\u7528\u3055\u308c\u307e\u3059\uff1a m \uff08 a \u222a b \uff09\uff09 \u2264 m \uff08 a \uff09\uff09 + m \uff08 b \uff09\uff09 {displaystyle mu\uff08acup b\uff09leq mu\uff08a\uff09+mu\uff08b\uff09} \u305f\u3081\u306b a \u3001 b {displaystyle a\u3001b} out H{displaystyle {mathcal {h}}} \u3068 a \u222a b \u2208 H{displaysyle acup bin {mathcal {h}}} \u3002 \u30a4\u30e0\u30ea\u30f3\u30b0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30ea\u30f3\u30b0\u3092\u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u3068\u3057\u3066\u9078\u629e\u3059\u308b\u5834\u5408\uff08\u5404\u30ea\u30f3\u30b0\u306f\u30cf\u30fc\u30d5\u30ea\u30f3\u30b0\u3067\u3042\u308b\u305f\u3081\uff09\u3001\u30cf\u30fc\u30d5\u30ea\u30f3\u30b0\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306b\u52a0\u3048\u3066\u3001\u6b21\u306e\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u306b\u52a0\u3048\u3066\uff1a \u6e1b\u7b97\u6027 \uff1a \u305f\u3081\u306b b \u2286 a {displaystyle bsubseteq a} \u3068 m \uff08 b \uff09\uff09 < \u221e {displaystyle mu\uff08b\uff09 b \uff09\uff09 = m \uff08 a \uff09\uff09  &#8211;  m \uff08 b \uff09\uff09 {displaystyle mu\uff08asetminus b\uff09= mu\uff08a\uff09-mu\uff08b\uff09} \u3002 a \u3001 b \u2208 R\u21d2 m \uff08 a \u222a b \uff09\uff09 + m \uff08 a \u2229 b \uff09\uff09 = m \uff08 a \uff09\uff09 + m \uff08 b \uff09\uff09 {displaystyle a\u3001bin {mathcal {r}} righttarrow mu\uff08acup b\uff09+mu\uff08acap b\uff09= mu\uff08a\uff09+mu\uff08b\uff09} \u3002 \u30b5\u30d6\u30a2\u30c0\u30a4\u30c6\u30a3\u30d6 \uff1a a i\u2208 R\uff08 \u79c1 = \u521d\u3081 \u3001 2 \u3001 &#8230; \u3001 n \uff09\uff09 \u21d2 m \uff08 \u22c3i=1nAi\uff09\uff09 \u2264 \u2211 i=1nm \uff08 a i\uff09\uff09 {displaystyle a_ {i} in {mathcal {r}} \u3002 a {displaystyle sigma} -SuperAdditivity \uff1a \u306a\u308c a i\u2208 R\uff08 \u79c1 = \u521d\u3081 \u3001 2 \u3001 &#8230; \uff09\uff09  {displaystyle a_ {i} in {mathcal {r}};\uff08i = 1,2\u3001dotsc\uff09}} \u30da\u30a2\u3067\u306f\u3001\u5426\u5b9a\u3057\u307e\u3059 \u22c3 i=1\u221ea i\u2208 R{displaystyle bigcup _ {i = 1}^{infty} a_ {i} in {mathcal {r}}}} \u3002\u305d\u306e\u5f8c\u3001\u6dfb\u52a0\u5264\u3068\u5358\u8abf\u3055\u304b\u3089\u7d9a\u304d\u307e\u3059 m \uff08 \u22c3i=1\u221eAi\uff09\uff09 \u2265 \u2211 i=1\u221em \uff08 a i\uff09\uff09 {displaystyle mu left\uff08bigcup _ {i = 1}^{infty} a_ {i} right\uff09geq sum _ {i = 1}^{infty} mu\uff08a_ {i}\uff09} \u3002 \u6edd m {displaystyle mu} \u6700\u5f8c\u306b\u3001\u307f\u3093\u306a\u306e\u305f\u3081\u306b a \u2208 R\u21d2 m \uff08 a \uff09\uff09 < \u221e {displaystyle ain {mathcal {r}} rightarrow mu\uff08a\uff09 i=1nAi)=\u2211k=1n(\u22121)k+1\u2211I\u2286{1,\u2026,n},|I|=k\u03bc(\u22c2i\u2208IAi){displaystyle mu left\uff08bigcup _ {i = 1}^{n} a_ {i} right\uff09= sum _ {k = 1}^{n}\uff08-1\uff09^{k+1} !! sum _ {isubseteq {1\u3001dotsc\u3001n}\u3001 } \u3068 a i\u2208 C{displaystyle a_ {i} in {mathcal {c}}} \u305f\u3081\u306b \u79c1 \u2208 { \u521d\u3081 \u3001 &#8230; \u3001 n } {displaystyle iin {1\u3001dotsc\u3001n}} \u3002 \u30b3\u30f3\u30c6\u30f3\u30c4\u306f\u610f\u5473\u3057\u307e\u3059 \u3064\u3044\u306b \u3001 \u3082\u3057\u3082 m \uff08 a \uff09\uff09 < \u221e {displaystyle mu\uff08a\uff09 N{displaystyle\uff08a_ {i}\uff09_ {iin mathbb {n}}}} \u304b\u3089 \u304a\u304a {displaystyle omega} \u306e c {displaystyle {mathcal {c}}} \u305d\u308c\u3092\u4e0e\u3048\u308b m \uff08 a \u79c1 \uff09\uff09 < \u221e {displaystyle mu\uff08a_ {i}\uff09 {displaystyle mu} \u534a\u8d70\u884c\u8ddd\u96e2 h {displaystyle {mathcal {h}}} \u30b3\u30f3\u30c6\u30f3\u30c4 m &#8216; {displaystyle mu &#8216;} \u306b h {displaystyle {mathcal {h}}} \u751f\u6210\u3055\u308c\u305f\u30ea\u30f3\u30b0 r {displaystyle {mathcal {r}}} \u69cb\u7bc9\u3059\u308b\u3002\u534a\u5206\u306e\u611b\u306e\u7279\u6027\u306e\u305f\u3081\u306b\u3001\u3059\u3079\u3066\u306e\u4eba\u306e\u305f\u3081\u306b\u3042\u308a\u307e\u3059 a \u2208 r {displaystyle ain {mathcal {r}}} \u30da\u30a2\u3067\u306f\u3001\u5206\u96e2\u6cd5\u306e\u91cf a \u521d\u3081 \u3001 a 2 \u3001 &#8230; \u3001 a m \u2208 h {displaystyle a_ {1}\u3001a_ {2}\u3001dotsc\u3001a_ {m} in {mathcal {h}}}} \u3068 a = \u22c3 j=1ma j{displaystyle textStyle a = bigcup _ {j = 1}^{m} a_ {j}} \u3002\u4e00\u3064 m &#8216; {displaystyle mu &#8216;} \u7d42\u3048\u305f m &#8216; \uff08 a \uff09\uff09 \uff1a= \u2211 j=1mm \uff08 a j\uff09\uff09 {displaystyle mu &#8216;\uff08a\uff09\uff1a= sum _ {j = 1}^{m} mu\uff08a_ {j}\uff09} \u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3068\u3001\u660e\u78ba\u306b\u6c7a\u5b9a\u3055\u308c\u305f\u7d9a\u7de8\u304c\u5f97\u3089\u308c\u307e\u3059 m &#8216; {displaystyle mu &#8216;} \u3002\u7d99\u7d9a m &#8216; {displaystyle mu &#8216;} \u307e\u3055\u306b\u305d\u3046\u3067\u3059 a {displaystyle sigma}  &#8211; \u6700\u7d42\u7684\u306b\u306fif m {displaystyle mu}  a {displaystyle sigma} -\u3064\u3044\u306b\u3002 \u78ba\u7387\u30b3\u30f3\u30c6\u30f3\u30c4 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30b3\u30f3\u30c6\u30f3\u30c4 m {displaystyle mu} a\u306b\u306a\u308a\u307e\u3059 \u78ba\u7387\u30b3\u30f3\u30c6\u30f3\u30c4 \u57fa\u672c\u7684\u306a\u6570\u91cf\u306e\u3068\u304d\u306b\u547c\u3073\u51fa\u3055\u308c\u307e\u3059 \u304a\u304a {displaystyle omega} \u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u3067 c {displaystyle {mathcal {c}}} \u542b\u307e\u308c\u3066\u3044\u307e\u3059 m \uff08 \u304a\u304a \uff09\uff09 = \u521d\u3081 {displaystyle mu\uff08omega\uff09= 1} \u9069\u7528\u53ef\u80fd\u3067\u3059 [4] \u3002 \u7f72\u540d\u3055\u308c\u305f\u30b3\u30f3\u30c6\u30f3\u30c4 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] a \u7f72\u540d\u3055\u308c\u305f\u30b3\u30f3\u30c6\u30f3\u30c4 \u6570\u91cf\u95a2\u6570\u3067\u3059 n {displaystyle not} \u6570\u91cf\u30b7\u30b9\u30c6\u30e0\u3067 m {displaystyle {mathcal {m}}} \u3001\u6709\u9650\u306e\u95a2\u9023\u4ed8\u3051\u306e\u89b3\u70b9\u304b\u3089\u5b8c\u4e86\u3057\u3001\u7a7a\u306e\u91cf\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 n \uff08 \u2205 \uff09\uff09 = 0 {displaystyle nu\uff08emptyset\uff09= 0} \u6570\u91cf\u95a2\u6570\u306e\u753b\u50cf\u91cf\u306f\u3067\u3059 [  &#8211;  \u221e \u3001 + \u221e \uff09\uff09 {displaystyle [-infty\u3001+infty\uff09} \u307e\u305f \uff08  &#8211;  \u221e \u3001 + \u221e ] {displaystyle\uff08-infty\u3001+infty]} \u3002 \u4ee5\u4e0b\u306f\u3001\u6dfb\u52a0\u5264\u3092\u8ffd\u52a0\u3057\u307e\u3059\u3002 n \uff08 a \u222a b \uff09\uff09 = n \uff08 a \uff09\uff09 + n \uff08 b \uff09\uff09 {displaystyle not\uff08acup b\uff09= no\uff08a\uff09+no\uff08b\uff09} \u5206\u96e2\u306e\u305f\u3081 a \u3001 b \u2208 M{displaystyle a\u3001bin {mathcal {m}}} [5] \u3002 \u30e6\u30eb\u30b2\u30f3\u30fb\u30a8\u30eb\u30b9\u30c8\u30ed\u30c3\u30c8\uff1a \u6e2c\u5b9a\u304a\u3088\u3073\u7d71\u5408\u7406\u8ad6 \u3002 6.\u3001\u4fee\u6b63\u7248\u3002 Springer-Verlag\u3001Berlin Heidelberg 2009\u3001ISBN 978-3-540-89727-9\u3001doi\uff1a 10,1007\/978-3-540-89728-6 \u3002  Achim Klenke\uff1a \u78ba\u7387\u7406\u8ad6 \u3002 3.\u30a8\u30c7\u30a3\u30b7\u30e7\u30f3\u3002 Springer-Verlag\u3001Berlin Heidelberg 2013\u3001ISBN 978-3-642-36017-6\u3001doi\uff1a 10,1007\/978-3-642-36018-3 \u3002  \u30af\u30e9\u30a6\u30b9D.\u30b7\u30e5\u30df\u30c3\u30c8\uff1a \u6e2c\u5b9a\u3068\u78ba\u7387 \u3002 2\u756a\u76ee\u3001\u30a8\u30c7\u30a3\u30b7\u30e7\u30f3\u3092\u901a\u3058\u3066\u3002 Springer-Verlag\u3001Heidelberg Dordrecht London New York 2011\u3001ISBN 978-3-642-21025-9\u3001doi\uff1a 10,1007\/978-3-642-21026-6 \u3002  \u2191  \u30b7\u30e5\u30df\u30c3\u30c8\uff1a \u6e2c\u5b9a\u3068\u78ba\u7387\u3002 2011\u5e74\u3001S\u300244\u3002  \u2191  \u30af\u30ec\u30f3\u30b1\uff1a \u78ba\u7387\u7406\u8ad6\u3002 2013\u3001S\u300212\u3002  \u2191  \u96fb\u6c17\uff1a \u6e2c\u5b9a\u304a\u3088\u3073\u7d71\u5408\u7406\u8ad6\u3002 2009\u5e74\u3001S\u300227\u3002  \u2191  \u30b7\u30e5\u30df\u30c3\u30c8\uff1a \u6e2c\u5b9a\u3068\u78ba\u7387\u3002 2011\u5e74\u3001S\u3002194\u3002  \u2191  \u96fb\u6c17\uff1a \u6e2c\u5b9a\u304a\u3088\u3073\u7d71\u5408\u7406\u8ad6\u3002 2009\u5e74\u3001S\u3002277\u3002  "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13386#breadcrumbitem","name":"\u30b3\u30f3\u30c6\u30f3\u30c4\uff08\u6e2c\u5b9a\u7406\u8ad6\uff09 &#8211; 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