monotone convergence theorem

GPTKB entity

Statements (18)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:alsoKnownAs gptkb:Beppo_Levi's_theorem
gptkbp:appliesTo non-negative measurable functions
gptkbp:describes limit of integrals of monotone sequences of 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
gptkbp:state If {f_n} is a sequence of non-negative measurable functions increasing pointwise to f, then the integral of f is the limit of the integrals of f_n
gptkbp:usedIn gptkb:Lebesgue_integration
gptkbp:yearProposed 1906
gptkbp:bfsParent gptkb:Dominated_convergence_theorem
gptkb:Fatou's_lemma
gptkbp:bfsLayer 6