Mendoza Casas, JoséPakhrou, Tijani2023-06-202023-06-202007-04-020021-904510.1016/j.jat.2006.09.003https://hdl.handle.net/20.500.14352/50160Let X be a Banach space, (Omega, Sigma, mu) a finite measure space, and L-1 (mu, X) the Banach space of X-valued Bochner mu-integrable functions defined on Omega endowed with its usual norm. Let us suppose that Sigma(0) is a sub-sigma-algebra of Sigma, and let mu(0) be the restriction of mu to Sigma(0). Given a natural number n, let N be a monotonous norm in R-n. It is shown that if X is reflexive then L-1 (mu(0), X) is N-simultaneously proximinal in L-1 (mu, X) in the sense of Fathi et al. [Best simultaneous approximation in L-p(I, E), J. Approx. Theory 116 (2002), 369-379]. Some examples and remarks related with N-simultaneous proximinality are also given.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0021904506001687http://www.sciencedirect.com/science/restricted access517.982.22Banach space.Geometría diferencial1204.04 Geometría Diferencial