Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
collections of sets
intervals in the real line |
| gptkbp:category |
theorems in analysis
|
| gptkbp:field |
measure theory
real analysis |
| gptkbp:firstPublished |
1908
|
| gptkbp:generalizes |
gptkb:Besicovitch_covering_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Vitali covering lemma
|
| gptkbp:namedAfter |
gptkb:Giuseppe_Vitali
|
| gptkbp:relatedTo |
Lebesgue measure
differentiation of integrals |
| gptkbp:sentence |
Given a set E of finite outer measure and a Vitali cover of E, there exists a countable disjoint subcollection whose union covers almost all of E.
|
| gptkbp:usedIn |
proof of Lebesgue differentiation theorem
proofs in geometric measure theory |
| gptkbp:bfsParent |
gptkb:Hardy–Littlewood_maximal_inequality
gptkb:Hardy–Littlewood_maximal_theorem |
| gptkbp:bfsLayer |
7
|