Monotone Convergence Theorem
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Beppo_Levi's_theorem
|
| gptkbp:appliesTo |
gptkb:Lebesgue_integral
|
| gptkbp:author |
gptkb:Beppo_Levi
|
| gptkbp:field |
mathematical analysis
measure theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Monotone Convergence Theorem
|
| gptkbp:introducedIn |
1906
|
| gptkbp:relatedTo |
gptkb:Dominated_Convergence_Theorem
gptkb:Fatou's_Lemma |
| gptkbp:state |
If a sequence of non-negative measurable functions increases pointwise to a limit, then the integral of the limit is the limit of the integrals.
|
| gptkbp:usedIn |
gptkb:probability_theory
real analysis integration theory |
| gptkbp:bfsParent |
gptkb:Lebesgue_integration
gptkb:Real_Analysis |
| gptkbp:bfsLayer |
7
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