Best N -Simultaneous Approximation in Lp(μ,X)

Let x be a banach space. let 1≤p<∞ and denote by lp(μ,x) the banach space of all x-valued bochner p-integrable functions on a certain positive complete σ-finite measure space (ω,σ,μ),endowed with the usual p-norm. in this paper,the theory of lifting is used to prove that,for any weakly compact subset w of x,the set lp (μ,w) is n-simultaneously proximinal in lp (μ,x) for any arbitrary monotonous norm n in rn. © 2017 tijani pakhrou.