Lebesgue differentiation theorem
GPTKB entity
Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
locally integrable functions
|
| gptkbp:concerns |
Lebesgue measure
differentiation of integrals |
| gptkbp:field |
real analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lebesgue differentiation theorem
|
| gptkbp:implies |
almost every point is a Lebesgue point
|
| gptkbp:namedAfter |
gptkb:Henri_Lebesgue
|
| gptkbp:publishedIn |
early 20th century
|
| gptkbp:state |
for locally integrable functions, the average value over balls converges to the function value almost everywhere
|
| gptkbp:usedIn |
harmonic analysis
measure theory |
| gptkbp:bfsParent |
gptkb:Hardy–Littlewood_maximal_function
|
| gptkbp:bfsLayer |
6
|