THE NEAR RADON-NIKODYM PROPERTY IN LEBESGUE-BOCHNER FUNCTION SPACES

摘要

Let X be a Banach space, (Ω, Σ, λ) be a finite measure space and 1 ≤ p ≤ ∞. We denote by L~p(λ, X) the Banach space of all (classes of) λ-measurable functions from Ω to X which are p-Bochner integrable with its usual norm ‖f‖_p = (∫ ‖f(?)‖~p dλ(ω))~(1/p). If X is the scalar field then L~p(λ, X) will be denoted by L~p(λ).