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 Best approximations in $L_p (S, X)$ Bull. Korean Math. Soc. 1999 Vol. 36, No. 3, 589-597 Mun Bae Lee, Sung Ho Park, and Hyang Joo Rhee Sogang University, Sogang University, Duksung Women's University Abstract : Let $G$ be a closed subspace of a Banach space $X$ and let $(S, \Omega, \mu)$ be a $\sigma$-finite measure space. It was known that $L_1(S,G)$ is proximinal in $L_1(S,X)$ if and only if $L_p(S,G)$ is proximinal in $L_p(S,X)$ for $1 In this article we show that this result remains true when "proximinal" is replaced by "Chebyshev". In addition, it is shown that if$G$is a proximinal subspace of$X$such that either$G$or the kernel of the metric projection$P_G$is separable then, for$0 Keywords : Chebyshev, proximinal, pointwise proximinal, proximity map, strongly measurable MSC numbers : 41A65, 46B20 Downloads: Full-text PDF