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About: Egorov's theorem
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It is also named Severini–Egoroff theorem or Severini–Egorov theorem, after Carlo Severini, an Italian mathematician, and Dmitri Egorov, a Russian physicist and geometer, who published independent proofs respectively in 1910 and 1911. 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title="Switch to /sparql endpoint"><i class="bi-box-arrow-up-right"></i> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div> <!-- /navbar --> <!-- page-header --> <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6"><b>About:</b> <a href="http://dbpedia.org/resource/Egorov's_theorem">Egorov's theorem</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> <span class="text-nowrap">An Entity of Type: <a href="http://dbpedia.org/class/yago/Abstraction100002137">Abstraction100002137</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions. It is also named Severini–Egoroff theorem or Severini–Egorov theorem, after Carlo Severini, an Italian mathematician, and Dmitri Egorov, a Russian physicist and geometer, who published independent proofs respectively in 1910 and 1911. Egorov's theorem can be used along with compactly supported continuous functions to prove Lusin's theorem for integrable functions.</p> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="de" >Der Satz von Jegorow ist ein Satz aus der Maßtheorie, der den Zusammenhang zwischen punktweiser Konvergenz μ-fast überall und fast gleichmäßiger Konvergenz zeigt. Teils finden sich auch die Schreibweisen Satz von Egorow, Satz von Egorov oder Satz von Egoroff, die auf eine Übertragung des Namens ins Englische oder Französische zurückzuführen sind. Der Satz ist nach Dmitri Fjodorowitsch Jegorow benannt, der ihn 1911 bewies. Die Aussage wurde bereits 1910 von gezeigt, weshalb sich auch die Benennung als Satz von Egorov-Severini (oder verwandte Schreibweisen) findet.</span><small> (de)</small></span></li> <li><span class="literal"><span property="dbo:abstract" lang="en" >In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions. It is also named Severini–Egoroff theorem or Severini–Egorov theorem, after Carlo Severini, an Italian mathematician, and Dmitri Egorov, a Russian physicist and geometer, who published independent proofs respectively in 1910 and 1911. Egorov's theorem can be used along with compactly supported continuous functions to prove Lusin's theorem for integrable functions.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="fr" >Le théorème d’Egoroff, nommé ainsi en hommage à Dmitri Egorov, un physicien et géomètre russe, établit une condition de convergence uniforme dans certains espaces mesurables. Ce théorème peut servir en particulier à montrer le théorème de Lusin pour les fonctions intégrables. Il s’agit en fait d’un résultat basique de théorie de l’intégration. Il permet en outre de donner une démonstration concise du théorème de convergence dominée.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="it" >In teoria della misura, il teorema di Egorov stabilisce una condizione per la convergenza uniforme di una successione di funzioni misurabili convergenti puntualmente. È stato dimostrato indipendentemente da Carlo Severini e Dmitrij Egorov, rispettivamente nel 1910 e 1911.</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ko" >측도론에서 예고로프 정리(Егоров定理, 영어: Egorov’s theorem)는 가측 함수에 대하여, 점별 수렴과 균등 수렴이 거의 일치한다는 정리이다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pl" >Twierdzenie Jegorowa – twierdzenie teorii miary mówiące, że każdy ciąg mierzalnych rzeczywistych funkcji prawie wszędzie skończonych określonych na wspólnej przestrzeni z miarą skończoną, który jest zbieżny prawie wszędzie do prawie wszędzie skończonej funkcji mierzalnej, jest do niej zbieżny prawie jednostajnie. Nazwa twierdzenia pochodzi od nazwiska Dimitrija Jegorowa. Littlewood wypowiedział nieformalnie twierdzenie Jegorowa w następujący sposób: zbieżne ciągi funkcji są nieomal jednostajnie zbieżne (tj. prawie jednostajnie zbieżne; zob. trzy zasady analizy rzeczywistej Littlewooda).</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ru" >Теоре́ма Его́рова утверждает, что последовательность измеримых функций, сходящаяся почти всюду на некотором множестве, сходится равномерно на достаточно большом его подмножестве.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pt" >Em matemática, o teorema de Egorov é um dos principais teoremas da teoria da medida. Recebe o nome em honra ao físico e geômetra russo Dmitri Egorov. O teorema estabelece um relação entre convergência quase-sempre e convergência uniforme em um espaço de medida finita.</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="uk" >Теорема Єгорова (теорема Северіні — Єгорова) — твердження в теорії міри про зв'язок збіжності майже всюди і рівномірної збіжності.</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="zh" >在测度论中，叶戈罗夫定理确立了一个可测函数的逐点收敛序列一致连续的条件。这个定理以俄国物理学家和几何学家德米特里·叶戈罗夫命名，他在1911年出版了该定理。 叶戈罗夫定理与紧支撑连续函数在一起，可以用来证明可积函数的卢津定理。</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink"><small>dbo:</small>wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" 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(en)</small></span></li> <li><span class="literal"><span property="dbp:authorLink" lang="en" >Lev Kudryavtsev</span><small> (en)</small></span></li> <li><span class="literal"><span property="dbp:authorLink" lang="en" >Wacław Sierpiński</span><small> (en)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/first"><small>dbp:</small>first</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:first" lang="en" >L.D.</span><small> (en)</small></span></li> <li><span class="literal"><span property="dbp:first" lang="en" >Frigyes</span><small> (en)</small></span></li> <li><span class="literal"><span property="dbp:first" lang="en" >Wacław</span><small> (en)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/id"><small>dbp:</small>id</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:id" 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href="http://www.w3.org/2000/01/rdf-schema#comment"><small>rdfs:</small>comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="de" >Der Satz von Jegorow ist ein Satz aus der Maßtheorie, der den Zusammenhang zwischen punktweiser Konvergenz μ-fast überall und fast gleichmäßiger Konvergenz zeigt. Teils finden sich auch die Schreibweisen Satz von Egorow, Satz von Egorov oder Satz von Egoroff, die auf eine Übertragung des Namens ins Englische oder Französische zurückzuführen sind. Der Satz ist nach Dmitri Fjodorowitsch Jegorow benannt, der ihn 1911 bewies. Die Aussage wurde bereits 1910 von gezeigt, weshalb sich auch die Benennung als Satz von Egorov-Severini (oder verwandte Schreibweisen) findet.</span><small> (de)</small></span></li> <li><span class="literal"><span property="rdfs:comment" lang="en" >In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions. It is also named Severini–Egoroff theorem or Severini–Egorov theorem, after Carlo Severini, an Italian mathematician, and Dmitri Egorov, a Russian physicist and geometer, who published independent proofs respectively in 1910 and 1911. Egorov's theorem can be used along with compactly supported continuous functions to prove Lusin's theorem for integrable functions.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="fr" >Le théorème d’Egoroff, nommé ainsi en hommage à Dmitri Egorov, un physicien et géomètre russe, établit une condition de convergence uniforme dans certains espaces mesurables. Ce théorème peut servir en particulier à montrer le théorème de Lusin pour les fonctions intégrables. Il s’agit en fait d’un résultat basique de théorie de l’intégration. Il permet en outre de donner une démonstration concise du théorème de convergence dominée.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="it" >In teoria della misura, il teorema di Egorov stabilisce una condizione per la convergenza uniforme di una successione di funzioni misurabili convergenti puntualmente. È stato dimostrato indipendentemente da Carlo Severini e Dmitrij Egorov, rispettivamente nel 1910 e 1911.</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ko" >측도론에서 예고로프 정리(Егоров定理, 영어: Egorov’s theorem)는 가측 함수에 대하여, 점별 수렴과 균등 수렴이 거의 일치한다는 정리이다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pl" >Twierdzenie Jegorowa – twierdzenie teorii miary mówiące, że każdy ciąg mierzalnych rzeczywistych funkcji prawie wszędzie skończonych określonych na wspólnej przestrzeni z miarą skończoną, który jest zbieżny prawie wszędzie do prawie wszędzie skończonej funkcji mierzalnej, jest do niej zbieżny prawie jednostajnie. Nazwa twierdzenia pochodzi od nazwiska Dimitrija Jegorowa. Littlewood wypowiedział nieformalnie twierdzenie Jegorowa w następujący sposób: zbieżne ciągi funkcji są nieomal jednostajnie zbieżne (tj. prawie jednostajnie zbieżne; zob. trzy zasady analizy rzeczywistej Littlewooda).</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ru" >Теоре́ма Его́рова утверждает, что последовательность измеримых функций, сходящаяся почти всюду на некотором множестве, сходится равномерно на достаточно большом его подмножестве.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pt" >Em matemática, o teorema de Egorov é um dos principais teoremas da teoria da medida. Recebe o nome em honra ao físico e geômetra russo Dmitri Egorov. O teorema estabelece um relação entre convergência quase-sempre e convergência uniforme em um espaço de medida finita.</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="uk" >Теорема Єгорова (теорема Северіні — Єгорова) — твердження в теорії міри про зв'язок збіжності майже всюди і рівномірної збіжності.</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="zh" >在测度论中，叶戈罗夫定理确立了一个可测函数的逐点收敛序列一致连续的条件。这个定理以俄国物理学家和几何学家德米特里·叶戈罗夫命名，他在1911年出版了该定理。 叶戈罗夫定理与紧支撑连续函数在一起，可以用来证明可积函数的卢津定理。</span><small> (zh)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="rdfs:label" lang="en" >Egorov's theorem</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="de" >Satz von Jegorow</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="it" >Teorema di Egorov</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="fr" >Théorème d'Egoroff</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ko" >예고로프 정리</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pl" >Twierdzenie Jegorowa</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pt" >Teorema de Egorov</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ru" >Теорема Егорова</span><small> (ru)</small></span></li> <li style="display:none;"><span 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