Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
Banach space-valued functions
|
| gptkbp:contrastsWith |
gptkb:Bochner_integral
|
| gptkbp:definedIn |
measurable functions
|
| gptkbp:defines |
A function f is Pettis integrable if for every continuous linear functional φ, the scalar function φ∘f is Lebesgue integrable and there exists an element x in the Banach space such that φ(x) equals the integral of φ∘f for all φ.
|
| gptkbp:field |
gptkb:mathematics
functional analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Pettis integral
|
| gptkbp:introducedIn |
1938
|
| gptkbp:isA |
generalization of the Lebesgue integral
|
| gptkbp:isWeakerThan |
Bochner integrability
|
| gptkbp:namedAfter |
gptkb:Billy_James_Pettis
|
| gptkbp:usedIn |
integration theory
vector measures |
| gptkbp:bfsParent |
gptkb:Bochner_integral
|
| gptkbp:bfsLayer |
6
|