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Let X be a Banach space and Ф be an Orlicz function. Denote by L^Ф(I,X) the space of X-valued (I)-integrable functions on the unit interval I equipped with the Luxemburg norm. For f1,f2,... ,fm ∈ L^Ф(I,X), a distance formula distv(f1,f2,... ,fm,L^Ф(I,G)) is presented, where G is a close subspace of X. Moreover, some existence and characterization results concerning the best simultaneous approximation of L^Ф (I, G) in L^Ф (I, X) axe given. 相似文献
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