Lebesgue's Dominated Convergence Theorem
GPTKB entity
Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
Lebesgue integrable functions
|
| gptkbp:field |
gptkb:mathematics
measure theory real analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Lebesgue's Dominated Convergence Theorem
|
| gptkbp:implies |
interchange of limit and integral
|
| gptkbp:namedAfter |
gptkb:Henri_Lebesgue
|
| gptkbp:publishedIn |
gptkb:Annali_di_Matematica_Pura_ed_Applicata
|
| gptkbp:requires |
pointwise convergence
existence of a dominating integrable function |
| gptkbp:sentence |
If a sequence of measurable functions converges pointwise to a function and is dominated by an integrable function, then the limit and the integral can be interchanged.
|
| gptkbp:year |
1904
|
| gptkbp:bfsParent |
gptkb:Dominated_Convergence_Theorem
|
| gptkbp:bfsLayer |
8
|