Best -Simultaneous Approximation in

Let be a Banach space. Let and denote by the Banach space of all -valued Bochner -integrable functions on a certain positive complete -finite measure space , endowed with the usual -norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset of , the set is -simultaneously proximinal in for any arbitrary monotonous norm in .

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