Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
measurable functions
sets of finite measure |
| gptkbp:field |
measure theory
real analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Egorov's theorem
|
| gptkbp:namedAfter |
gptkb:Dmitri_Egorov
|
| gptkbp:publishedIn |
gptkb:Mathematical_Annalen
|
| gptkbp:relatedTo |
gptkb:Lusin's_theorem
uniform convergence convergence almost everywhere |
| gptkbp:sentence |
If a sequence of measurable functions converges almost everywhere on a set of finite measure, then for every ε > 0, there exists a subset of measure less than ε outside of which the convergence is uniform.
|
| gptkbp:yearProposed |
1911
|
| gptkbp:bfsParent |
gptkb:Dmitri_Egorov
gptkb:Luzin's_theorem |
| gptkbp:bfsLayer |
7
|