[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10690#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10690","headline":"\u500b\u5225\u306e\u30a8\u30eb\u30b4\u30fc\u30c9\u30bb\u30c3\u30c8-Wikipedia","name":"\u500b\u5225\u306e\u30a8\u30eb\u30b4\u30fc\u30c9\u30bb\u30c3\u30c8-Wikipedia","description":"before-content-x4 \u500b\u3005\u306e\u6642\u4ee3 \u306f\u3001ERA\u7406\u8ad6\u306e\u91cd\u8981\u306a\u6587\u3067\u3042\u308a\u3001\u5b89\u5b9a\u7cfb\u3068\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306e\u7406\u8ad6\u306e\u5883\u754c\u5730\u57df\u306b\u304a\u3051\u308b\u6570\u5b66\u306e\u30b5\u30d6\u30a8\u30ea\u30a2\u3067\u3059\u3002\u307e\u305f\u306f\u3001\u500b\u3005\u306e\u30a8\u30eb\u30b4\u30fc\u30c9\u30bb\u30c3\u30c8\u3082\u305d\u3046\u3067\u3059 Birkhoff\u306eErgoden\u30bb\u30c3\u30c8 \u307e\u305f \u30dd\u30a4\u30f3\u30c8ergodenzing \u547c\u3073\u51fa\u3055\u308c\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3001\u4f9d\u5b58\u3059\u308b\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u306b\u5bfe\u3057\u3066\u591a\u6570\u306e\u5f37\u3044\u6cd5\u5247\u306e\u5f62\u5f0f\u3092\u63d0\u4f9b\u3057\u3001\u7d71\u8a08\u7269\u7406\u5b66\u306e\u6642\u4ee3\u4eee\u8aac\u306e\u6570\u5b66\u7684\u6839\u62e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002 \u3053\u306e\u5224\u6c7a\u306f\u30011931\u5e74\u306b\u30b8\u30e7\u30fc\u30b8\u30fb\u30c7\u30a4\u30d3\u30c3\u30c9\u30fb\u30d3\u30eb\u30db\u30d5\u306b\u3088\u3063\u3066\u8a3c\u660e\u3055\u308c\u3001\u305d\u306e\u5f8c\u3082\u5f7c\u306f\u6307\u540d\u3055\u308c\u307e\u3057\u305f\u3002 [\u521d\u3081] Hopf\u306e\u6700\u5927Ergodenlemmas\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u8a3c\u62e0\u304c\u53ef\u80fd\u3067\u3059\u3002\u52a0\u3048\u3066 Lp{displaystyle {mathcal {l}}^{p}} after-content-x4 -gode\u30bb\u30c3\u30c8\u306f\u3001\u3042\u307e\u308a\u52b4\u529b\u3092\u304b\u3051\u305a\u306b\u500b\u3005\u306e\u6642\u4ee3\u304b\u3089\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u305d\u3046\u3067\u3059 \u30d0\u30c4 {displaystyle x} \u7d71\u5408\u53ef\u80fd\u306a\u30e9\u30f3\u30c0\u30e0\u5909\u6570\uff08\u3064\u307e\u308a\u3001\u6709\u9650\u306e\u671f\u5f85\u5024\u304c\u3042\u308a\u307e\u3059\uff09\u3068","datePublished":"2022-03-09","dateModified":"2022-03-09","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:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/74656e06707b0d5ba1cd9fbe51155b561d082e23","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/74656e06707b0d5ba1cd9fbe51155b561d082e23","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10690","wordCount":4854,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u500b\u3005\u306e\u6642\u4ee3 \u306f\u3001ERA\u7406\u8ad6\u306e\u91cd\u8981\u306a\u6587\u3067\u3042\u308a\u3001\u5b89\u5b9a\u7cfb\u3068\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306e\u7406\u8ad6\u306e\u5883\u754c\u5730\u57df\u306b\u304a\u3051\u308b\u6570\u5b66\u306e\u30b5\u30d6\u30a8\u30ea\u30a2\u3067\u3059\u3002\u307e\u305f\u306f\u3001\u500b\u3005\u306e\u30a8\u30eb\u30b4\u30fc\u30c9\u30bb\u30c3\u30c8\u3082\u305d\u3046\u3067\u3059 Birkhoff\u306eErgoden\u30bb\u30c3\u30c8 \u307e\u305f \u30dd\u30a4\u30f3\u30c8ergodenzing \u547c\u3073\u51fa\u3055\u308c\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3001\u4f9d\u5b58\u3059\u308b\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u306b\u5bfe\u3057\u3066\u591a\u6570\u306e\u5f37\u3044\u6cd5\u5247\u306e\u5f62\u5f0f\u3092\u63d0\u4f9b\u3057\u3001\u7d71\u8a08\u7269\u7406\u5b66\u306e\u6642\u4ee3\u4eee\u8aac\u306e\u6570\u5b66\u7684\u6839\u62e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u5224\u6c7a\u306f\u30011931\u5e74\u306b\u30b8\u30e7\u30fc\u30b8\u30fb\u30c7\u30a4\u30d3\u30c3\u30c9\u30fb\u30d3\u30eb\u30db\u30d5\u306b\u3088\u3063\u3066\u8a3c\u660e\u3055\u308c\u3001\u305d\u306e\u5f8c\u3082\u5f7c\u306f\u6307\u540d\u3055\u308c\u307e\u3057\u305f\u3002 [\u521d\u3081] Hopf\u306e\u6700\u5927Ergodenlemmas\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u8a3c\u62e0\u304c\u53ef\u80fd\u3067\u3059\u3002\u52a0\u3048\u3066 Lp{displaystyle {mathcal {l}}^{p}}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4-gode\u30bb\u30c3\u30c8\u306f\u3001\u3042\u307e\u308a\u52b4\u529b\u3092\u304b\u3051\u305a\u306b\u500b\u3005\u306e\u6642\u4ee3\u304b\u3089\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u305d\u3046\u3067\u3059 \u30d0\u30c4 {displaystyle x} \u7d71\u5408\u53ef\u80fd\u306a\u30e9\u30f3\u30c0\u30e0\u5909\u6570\uff08\u3064\u307e\u308a\u3001\u6709\u9650\u306e\u671f\u5f85\u5024\u304c\u3042\u308a\u307e\u3059\uff09\u3068        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4t {displaystylet} \u57fa\u790e\u3068\u306a\u308b\u78ba\u7387\u7a7a\u9593\u3067\u306e\u7537\u6027\u306e\u5909\u63db \uff08 \u304a\u304a \u3001 A\u3001 p \uff09\uff09 {displaystyle\uff08omega\u3001{mathcal {a}}\u3001p\uff09} \uff08d\u3002h\u3002 p \uff08 t \u22121\uff08 a \uff09\uff09 \uff09\uff09 = p \uff08 a \uff09\uff09 {displaystyle P\uff08t^{ –  1}\uff08a\uff09\uff09= p\uff08a\uff09} \u3059\u3079\u3066\u306e\u305f\u3081\u306b a {displaystyle a} \u306e        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4A{displaystyle {mathcal {a}}} \uff09\u3002\u305d\u306e\u5f8c\u3001\u30d5\u30a1\u30f3\u30c9\u306f\u53ce\u675f\u3057\u307e\u3059 1n\u2211i=1n\u30d0\u30c4 \u2218 Ti\uff08 \u304a\u304a \uff09\uff09 {displaystyle {frac {1} {n}} sum _ {i = 1}^{n} xcirc t^{i}\uff08omega\uff09} \u305f\u3081\u306b n \u2192 \u221e {displaystyle nto infty} \u30e9\u30f3\u30c0\u30e0\u5909\u6570\u306b\u5bfe\u3057\u3066\u307b\u307c\u5b89\u5168\u3067\u3059 \u3068 {displaystyle y} \u3002 \u3068 {displaystyle y} \u306e\u305d\u308c\u306b\u95a2\u3057\u3066\u6e2c\u5b9a\u53ef\u80fd\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 t {displaystylet}  – \u30a4\u30f3\u30d0\u30ea\u30a2\u30f3\u306e\u610f\u5473 a {displaystyle a} \uff08d\u3002h\u3002 t \u22121\uff08 a \uff09\uff09 = a {displaystyle t^{ –  1}\uff08a\uff09= a} \uff09\u03c3\u4ee3\u6570\u3092\u751f\u6210\u3057\u307e\u3057\u305f T{displaystyle {mathcal {t}}} \u9078\u629e\u3067\u304d\u3001\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024\u3068\u3057\u3066\u9078\u629e\u3067\u304d\u307e\u3059 \u3068 [ \u30d0\u30c4 | T] {displaystyle e [x | {mathcal {t}}]} \u4ee3\u8868\u3059\u308b\u3002 \u3082\u3057\u3082 t {displaystylet} \u30a8\u30eb\u30b4\u30b8\u30c3\u30af\u3067\u3059\u3001\u305d\u3046\u3067\u3059 \u3068 {displaystyle y} \u307b\u307c\u78ba\u5b9f\u306b\u3001\u306e\u671f\u5f85\u5024\u306f\u4e00\u5b9a\u3067\u3059 \u30d0\u30c4 {displaystyle x} \u3002 \u30e9\u30f3\u30c0\u30e0\u5909\u6570 \u3068 i= \u30d0\u30c4 \u2218 t i{displaystyle y_ {i} = xcirc t^{i}} \uff08 \u79c1 = \u521d\u3081 \u3001 2 \u3001 … {displaystyle i = 1,2\u3001dots} \uff09\u9759\u6b62\u3057\u305f\u78ba\u7387\u30d7\u30ed\u30bb\u30b9\u3092\u5f62\u6210\u3057\u307e\u3059\u3002 H. \uff08 \u3068 2\u3001 \u3068 3\u3001 … \uff09\uff09 {displaystyle\uff08y_ {2}\u3001y_ {3}\u3001dots\uff09} \u306e\u3088\u3046\u306b\u5206\u5e03\u3057\u3066\u3044\u307e\u3059 \uff08 \u3068 1\u3001 \u3068 2\u3001 … \uff09\uff09 {displaystyle\uff08y_ {1}\u3001y_ {2}\u3001dots\uff09} \u3002\u9006\u306b\u3001\u3059\u3079\u3066\u306e\u5165\u9662\u60a3\u8005\u306e\u78ba\u7387\u7684\u30d7\u30ed\u30bb\u30b9\u306f\u53ef\u80fd\u3067\u3059 \uff08 \u3068 i\uff09\uff09 i\u22651{displaystyle\uff08y_ {i}\uff09_ {igeq 1}} \u3042\u306a\u305f\u304c\u305d\u308c\u3092\u60f3\u5b9a\u3059\u308b\u3068\u304d\u3001\u3053\u306e\u3088\u3046\u306b\u8868\u73fe\u3057\u3066\u304f\u3060\u3055\u3044 \u304a\u304a = R{1,2,\u2026}{displaystyle omega = mathbb {r} ^{{1,2\u3001dots}}}} \u3068 \u3068 i{displaystyle y_ {i}} \u30d5\u30a9\u30fc\u30e0\u304b\u3089 \u3068 i\uff08 \u304a\u304a 1\u3001 \u304a\u304a 2\u3001 … \uff09\uff09 = \u304a\u304a i{displaystyle y_ {i}\uff08omega _ {1}\u3001omega _ {2}\u3001dots\uff09= omega _ {i}} \u306f\u3002 \uff08\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306f\u3001 R{1,2,\u2026}{displaystyle mathbb {r} ^{{1,2\u3001dots}}}} \u306e\u753b\u50cf\u6e2c\u5b9a\u3067 \uff08 \u3068 1\u3001 \u3068 2\u3001 … \uff09\uff09 {displaystyle\uff08y_ {1}\u3001y_ {2}\u3001dots\uff09} \u305d\u308c\u4ee5\u5916\u306e \u304a\u304a {displaystyle omega} \u3068 p {displaystyle p} \u898b\u3066\u304f\u3060\u3055\u3044\u3002\uff09\u305d\u3053\u306b\u3042\u308a\u307e\u3059 \u30d0\u30c4 \uff08 \u304a\u304a 1\u3001 \u304a\u304a 2\u3001 … \uff09\uff09 = \u304a\u304a 1{displaystyle X\uff08omega {1}\u3001omega _ {2}\u3001dots\uff09= omega _ {1}} \u3001\u304a\u3088\u3073\u5de6\u30ea\u30d5\u30c8\u3001 \uff08 \u304a\u304a 1\u3001 \u304a\u304a 2\u3001 … \uff09\uff09 {displaystyle\uff08omega _ {1}\u3001omega _ {2}\u3001dots\uff09} \u306e\u4e0a \uff08 \u304a\u304a 2\u3001 \u304a\u304a 3\u3001 … \uff09\uff09 {displaystyle\uff08omega _ {2}\u3001omega _ {3}\u3001dots\uff09} \u30e1\u30a4\u30c9\u3001\u52a9\u6210\u91d1\u3092\u6442\u53d6\u3059\u308b\u5909\u63db\u3002 \u306e\u5834\u5408 \u3068 i{displaystyle y_ {i}} ERA\u30bb\u30c3\u30c8\u306b\u5f93\u3063\u3066\u53ce\u675f\u3059\u308b\u6709\u9650\u306e\u671f\u5f85\u5024\u3092\u6301\u3063\u3066\u3044\u308b 1n\u2211i=1nYi\uff08 \u304a\u304a \uff09\uff09 {displaystyle {frac {1} {n}} sum _ {i = 1}^{n} y_ {i}\uff08omega\uff09} \u305f\u3081\u306b n \u2192 \u221e {displaystyle nto infty} \u30e9\u30f3\u30c0\u30e0\u5909\u6570\u306b\u5bfe\u3057\u3066\u307b\u307c\u5b89\u5168\u3067\u3059 \u3068 {displaystyle y} \u3002\u3053\u308c\u304c\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024\u3067\u3059 \u3068 [ \u3068 i| T] {displaystyle e [y_ {i} | {mathcal {t}}]} \u305d\u308c\u305e\u308c\u306e \u3068 i{displaystyle y_ {i}} \u3002ergodicity\u304c\u5229\u7528\u53ef\u80fd\u306a\u5834\u5408\u3001 \u3068 {displaystyle y} \u307b\u307c\u5b89\u5168\u306b\u4e00\u5b9a\u3001\u3064\u307e\u308aH. 1n\uff08 Y1+ \u22ef + Yn\uff09\uff09 \u2192 \u3068 [ Yi] {displaystyle {frac {1} {n}}\uff08y_ {1} +dots +y_ {n}\uff09\u3001to\u3001e [y_ {i}]} \u304b\u306a\u308a\u78ba\u5b9f\u306a   \uff08 \u79c1 \u2265 \u521d\u3081 {displaystyle igeq 1} \u3069\u308c\u3067\u3082\uff09\u3002 \u2191  G. D. Birkhoff\uff1a \u30a8\u30eb\u30b4\u30fc\u30c9\u306e\u5b9a\u7406\u306e\u8a3c\u62e0 \u3001\uff081931\uff09\u3001Proc Natl Acad Sci U S A\u3001 17 S. 656\u2013660\u3002 PDF\u3002 AT\uff1apas.org        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@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\/10690#breadcrumbitem","name":"\u500b\u5225\u306e\u30a8\u30eb\u30b4\u30fc\u30c9\u30bb\u30c3\u30c8-Wikipedia"}}]}]