Compactness in the Lebesgue-Bochner spaces Lp(μ;X)
Abstract
Let (,μ) be a finite measure space, X a Banach space, and let 1 p<∞. The aim of this paper is to give an elementary proof of the Diaz--Mayoral theorem that a subset V of Lp(μ;X) is relatively compact if and only if it is uniformly p-integrable, uniformly tight, and scalarly relatively compact.
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