학술논문
ON THE PETTIS INTEGRABILITY
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- 영문명
- 발행기관
- 충청수학회
- 저자명
- JIN YEE KIM
- 간행물 정보
- 『Journal of the Chungcheong Mathematical Society』Volume 8, No. 1, 111~117쪽, 전체 7쪽
- 주제분류
- 자연과학 > 자연과학일반
- 파일형태
- 발행일자
- 1995.06.30
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국문 초록
영문 초록
A function f : Ω → x is called intrinsically-separable valued if there exists E ∈ Σ with μ(E) = 0 such that f(Ω - E) is a separable in X. For a given Dunford integrable function f : Ω → X and a weakly compact operator T, we show that if f is intrinsically-separable valued, then f is Pettis integrable, and if there exists a sequence (fn) of Dunford integrable and intrinsically-separable valued functions from Ω into X such that for each x* ∈ X*, x* fn → x* f a.e., then f is Pettis integrable. We show that a function f is Pettis integrable if and only if for each E ∈ Σ, F(E) is weak*-continuous on Bx* if and only if for each E ∈ Σ, M = {x* ∈ X* : F(E)(x*) = 0} is weak*-closed.
목차
ABSTRACT
1. Introduction
2. Pettis Integrability
3. Properties of The Pettis Integrability
REFERENCES
키워드
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