@prefix p: <http://www.wikidata.org/prop/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix schema1: <http://schema.org/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix wd: <http://www.wikidata.org/entity/> .
@prefix wds: <http://www.wikidata.org/entity/statement/> .
@prefix wdt: <http://www.wikidata.org/prop/direct/> .
@prefix wdtn: <http://www.wikidata.org/prop/direct-normalized/> .
@prefix wikibase: <http://wikiba.se/ontology#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

wd:Q2275191 rdfs:label "Teorema de diferenciació de Lebesgue"@ca,
        "Lebesgue differentiation theorem"@en,
        "derivoteoremo de Lebesgue"@eo,
        "Lebesguen differentioituvuuslause"@fi,
        "théorème de différentiation de Lebesgue"@fr,
        "משפט הדיפרנציאציה של לבג"@he,
        "Teorema di Lebesgue"@it,
        "ルベーグの微分定理"@ja,
        "르베그 미분가능성 정리"@ko,
        "Lebesgue differentiation theorem"@nl,
        "Teorema ëd diferensiassion ëd Lebesgue"@pms,
        "Teorema da diferenciação de Lebesgue"@pt,
        "теорема дифференцирования Лебега"@ru,
        "Теорема Лебега про диференціювання"@uk,
        "勒貝格微分定理"@zh,
        "勒贝格微分定理"@zh-hans,
        "勒貝格微分定理"@zh-hant,
        "勒貝格微分定理"@zh-hk ;
    schema1:dateModified "2026-11-05T15:56:58+00:00"^^xsd:dateTime ;
    schema1:description "teorema matemàtic"@ca,
        "mathematischer Satz"@de,
        "in real analysis, the theorem that, for almost every point, the value of an integrable function is the limiting average taken around the point"@en,
        "la teoremo, ke la valoro de integreblafunkcio ĉe iu punkto egalas preskaŭ ĉie la limeson (de malgrandiĝanta radiuso) de la averaĝo de la funkcio en globo ĉe tiu punkto"@eo,
        "théorème mathématique"@fr ;
    schema1:version 2565061509 ;
    wikibase:identifiers 2 ;
    wikibase:sitelinks 10 ;
    wikibase:statements 13 ;
    skos:altLabel "Théorème de différenciation de Lebesgue"@fr ;
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    p:P31 wds:Q2275191-EBB732E7-9B35-4880-B6D8-39252832733F ;
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    p:P6104 wds:Q2275191-AD0062F2-F100-4DC7-A25F-74B9AE3A7CDC ;
    p:P6366 wds:Q2275191-00E7AAE0-19E4-485C-91E5-5A36644EC5E5 ;
    p:P646 wds:Q2275191-0ACA7C9C-526E-494A-AAAA-DDE64872F51B ;
    p:P7235 wds:Q2275191-189d04ca-4a12-905f-b78e-3780fe7c1405,
        wds:Q2275191-914c7813-429d-c18a-4f8c-0034c0691d2f,
        wds:Q2275191-adbe2a1e-4db2-4ce7-3331-a53f674e9d50,
        wds:Q2275191-b19f1e9d-4e29-2233-bcae-693a32d426cf,
        wds:Q2275191-b40c0eea-4e82-740b-5aec-84a92664bd10,
        wds:Q2275191-e8778c22-4db4-ee83-fd98-34de500ea079 ;
    wdtn:P6366 <https://makg.org/entity/2778742007> ;
    wdt:P138 wd:Q206005 ;
    wdt:P2534 "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munder><mo form=\"prefix\">lim</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>r</mi><mo stretchy=\"false\" accent=\"false\">→</mo><mn>0</mn></mrow></mrow></munder><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msub><mo stretchy=\"false\">∫</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msub><mo data-mjx-texclass=\"OP\" mathvariant=\"normal\">ball</mo><mrow data-mjx-texclass=\"ORD\"><mi>r</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo></mrow></mrow></msub><mi>f</mi><mspace width=\"0.167em\"></mspace><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d</mi></mrow><mi>μ</mi></mrow></mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>μ</mi><mo stretchy=\"false\">(</mo><msub><mo data-mjx-texclass=\"OP\" mathvariant=\"normal\">ball</mo><mrow data-mjx-texclass=\"ORD\"><mi>r</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo></mrow></mrow></mfrac></mrow><mo stretchy=\"false\">=</mo><mi>f</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mspace width=\"1em\"></mspace><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">a</mi><mo mathvariant=\"normal\" stretchy=\"false\">.</mo><mi mathvariant=\"normal\">e</mi><mo mathvariant=\"normal\" stretchy=\"false\">.</mo></mrow></mrow></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P31 wd:Q65943 ;
    wdt:P361 wd:Q944443 ;
    wdt:P6104 wd:Q8487137 ;
    wdt:P6366 "2778742007" ;
    wdt:P646 "/m/0f3jwj" ;
    wdt:P7235 "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>f</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>r</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>μ</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mo data-mjx-texclass=\"OP\" mathvariant=\"normal\">ball</mo></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mo stretchy=\"false\">∫</mo></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" class=\"mwe-math-element mwe-math-element-inline\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">a</mi><mo mathvariant=\"normal\" stretchy=\"false\">.</mo><mi mathvariant=\"normal\">e</mi><mo mathvariant=\"normal\" stretchy=\"false\">.</mo></mrow></mrow></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> .

