Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
non-negative measurable functions
|
| gptkbp:field |
measure theory
real analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Fatou's lemma
|
| gptkbp:introducedIn |
1906
|
| gptkbp:namedAfter |
gptkb:Pierre_Fatou
|
| gptkbp:publishedIn |
gptkb:Annales_de_la_Faculté_des_Sciences_de_Toulouse
|
| gptkbp:relatedTo |
gptkb:dominated_convergence_theorem
gptkb:monotone_convergence_theorem gptkb:Lebesgue_integration |
| gptkbp:sentence |
The integral of the lim inf of a sequence of non-negative measurable functions is less than or equal to the lim inf of the integrals.
|
| gptkbp:usedIn |
proof of the dominated convergence theorem
proof of the monotone convergence theorem |
| gptkbp:bfsParent |
gptkb:Measure_Theory
|
| gptkbp:bfsLayer |
5
|