학술저널
PETTIS INTEGRABILITY
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 8, No. 1
-
1995.06161 - 166 (6 pages)
- 0
Let (Ω, Σ, μ) be a finite perfect measure space, and let f : Ω → X be strongly measurable. f is Pettis integrable if and only if there is a sequence (fn) of Pettis integrable functions from n into X such that (a) there is a positive increasing function φ defined on (0, ∞) such that limt→∞ φ(t)/t=∞ and sup fΩφ(│x* fn│) dμ < ∞ for each x* ∈ Bx*, n ∈ N, and (b) for each x* ∈ X*, limn→∞x* fn = x* fa.e..
ABSTRACT
1. Preliminaries
2. Pettis Integrability
REFERENCES
(0)
(0)