Some density properties of the closed unit ball of L_1

摘要

In this paper we present some properties on the densifiability of certain subsets of L_1. In particular, we prove that the closed unit ball B_1 in L_1 can be filled by weak curves with arbitrarily small density in the same way as it is done in the unit ball of a finite-dimensional space, but a very peculiar detail. Some weak density properties of the set D, of all probability functions of L_1, are used to approach a solution of an infinite-dimensional global optimization problem, posed on V, by means of solutions of one-dimensional global optimization problems posed on each curve that densities D.