Lebesgue's differentiation theorem
GPTKB entity
Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
locally integrable functions
|
| gptkbp:concerns |
differentiation of integrals
|
| gptkbp:field |
real analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lebesgue's differentiation theorem
|
| gptkbp:namedAfter |
gptkb:Henri_Lebesgue
|
| gptkbp:relatedTo |
gptkb:Hardy–Littlewood_maximal_function
gptkb:Vitali_covering_theorem Lebesgue measure |
| gptkbp:sentence |
For a locally integrable function f on R^n, the average value of f over balls centered at x converges to f(x) almost everywhere as the radius shrinks to zero.
|
| gptkbp:yearProved |
1904
|
| gptkbp:bfsParent |
gptkb:Luzin's_theorem
|
| gptkbp:bfsLayer |
7
|