Dominated Convergence Theorem
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Lebesgue's_Dominated_Convergence_Theorem
|
| gptkbp:appliesTo |
gptkb:Lebesgue_integral
|
| gptkbp:field |
mathematical analysis
measure theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Dominated Convergence Theorem
|
| gptkbp:introducedIn |
1904
|
| gptkbp:namedAfter |
gptkb:Henri_Lebesgue
|
| gptkbp:publishedIn |
gptkb:Annales_de_la_Faculté_des_Sciences_de_Toulouse
|
| gptkbp:relatedTo |
gptkb:Monotone_Convergence_Theorem
gptkb:Fatou's_Lemma |
| gptkbp:state |
If a sequence of measurable functions converges pointwise and is dominated by an integrable function, then the limit function is integrable and the limit of the integrals equals the integral of the limit.
|
| gptkbp:usedIn |
gptkb:probability_theory
functional analysis statistics |
| gptkbp:bfsParent |
gptkb:Lebesgue_integration
gptkb:Real_Analysis |
| gptkbp:bfsLayer |
7
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