Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
non-negative measurable functions
|
| gptkbp:category |
theorems in analysis
|
| gptkbp:countryOfPublication |
gptkb:French
|
| gptkbp:field |
measure theory
real analysis |
| gptkbp:firstPublished |
1906
|
| https://www.w3.org/2000/01/rdf-schema#label |
Fatou's Lemma
|
| gptkbp:namedAfter |
gptkb:Pierre_Fatou
|
| gptkbp:relatedTo |
gptkb:Dominated_Convergence_Theorem
gptkb:Monotone_Convergence_Theorem |
| 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:usedFor |
proving convergence theorems
|
| gptkbp:usedIn |
gptkb:Lebesgue_integration
|
| gptkbp:bfsParent |
gptkb:Dominated_Convergence_Theorem
gptkb:Monotone_Convergence_Theorem |
| gptkbp:bfsLayer |
8
|