Monotone convergence theorem
GPTKB entity
Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Beppo_Levi's_theorem
|
| gptkbp:appliesTo |
gptkb:Lebesgue_integral
|
| gptkbp:describes |
limit of increasing sequence of measurable functions
|
| gptkbp:field |
gptkb:mathematics
measure theory real analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Monotone convergence theorem
|
| gptkbp:namedAfter |
gptkb:Beppo_Levi
|
| gptkbp:publishedIn |
gptkb:Annali_di_Matematica_Pura_ed_Applicata
|
| gptkbp:relatedTo |
gptkb:Dominated_convergence_theorem
gptkb:Fatou's_lemma gptkb:Lebesgue_integration |
| gptkbp:state |
If {f_n} is a sequence of non-negative measurable functions increasing to f, then the integral of f is the limit of the integrals of f_n
|
| gptkbp:usedIn |
gptkb:probability_theory
ergodic theory functional analysis statistics |
| gptkbp:yearProposed |
1906
|
| gptkbp:bfsParent |
gptkb:Measure_Theory
|
| gptkbp:bfsLayer |
5
|