학술저널
A Characterization of The Strong Measurability via Oscillation
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 7, No. 1
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1994.0659 - 67 (9 pages)
- 0
Let (Ω, Σ, μ) be a measure space. A function f:Ω→X is said to be equioscillated if for each set A ∈ Σ of positive measure and for each ∈ > 0, there is a measurable subset B of A of positive measure such that the inequality supωϵΒ x* f(ω) - infωϵΒ x* f(ω) < ϵ holds for every x* with ∥x*∥ < 1. Strong measurability of a vector valued function is characterized using equioscillation.
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