On reflexivity of the Bochner space $L^p$ (µ, E) for arbitrary µ

Abstract

Let (Ω, A, µ) be a finite positive measure space, E a Banach space, and 1 < p < ∞. It is known that theBochner space $L^p$(µ, E) is reflexive if and only if E is reflexive. It is also known that L ( $L^1$(µ), E) = $L^infty$ (µ, E) if andonly if E has the Radon–Nikod´ym property. In this study, as an application of hyperstonean spaces, these results areextended to arbitrary measures by replacing the given measure space by an equivalent perfect one.