Lebesgue differentiation theorem
in real analysis, the theorem that, for almost every point, the value of an integrable function is the limiting average taken around the point
| rdfs:label |
"Lebesgue differentiation theorem"@en
|
|
skos:alt |
"Théorème de différenciation de Lebesgue"@fr |
| schema:description |
"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
|
|
schema:date |
"2026-11-05T15:56:58+00:00"^^xsd:dateTime |
| schema:version | 2565061509 |
| wikibase:identifiers | 2 |
| wikibase:sitelinks | 10 |
| wikibase:statements | 13 |
| p:P138 | wd:statement/Q2275191-b108138b-4d47-65f2-cbe2-3159210683e6 |
| p:P2534 | wd:statement/Q2275191-2788404b-4287-d86f-0d54-65164d49a8a3 |
| p:P31 | wd:statement/Q2275191-EBB732E7-9B35-4880-B6D8-39252832733F |
| p:P361 | wd:statement/Q2275191-20D00B64-A1E9-4C83-8E76-8136AA177EC7 |
| p:P6104 | wd:statement/Q2275191-AD0062F2-F100-4DC7-A25F-74B9AE3A7CDC |
| p:P6366 | wd:statement/Q2275191-00E7AAE0-19E4-485C-91E5-5A36644EC5E5 |
| p:P646 | wd:statement/Q2275191-0ACA7C9C-526E-494A-AAAA-DDE64872F51B |
| p:P7235 | wd:statement/Q2275191-189d04ca-4a12-905f-b78e-3780fe7c1405 |
| wd:statement/Q2275191-914c7813-429d-c18a-4f8c-0034c0691d2f | |
| wd:statement/Q2275191-adbe2a1e-4db2-4ce7-3331-a53f674e9d50 | |
| wd:statement/Q2275191-b19f1e9d-4e29-2233-bcae-693a32d426cf | |
| wd:statement/Q2275191-b40c0eea-4e82-740b-5aec-84a92664bd10 | |
| wd:statement/Q2275191-e8778c22-4db4-ee83-fd98-34de500ea079 | |
|
p:direct- |
<https:/ |
| wdt:P138 | Henri Lebesgue |
| 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 | theorem |
| wdt:P361 | list of theorems |
| wdt:P6104 | WikiProject Mathematics |
| 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 |
Download as: