Some density properties of the closed unit ball of L1

In this paper we present some properties on the densifiability of certain subsets of L1. In particular, we prove that the closed unit ball B1 in L1 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 L1, are used to approach a solution of an infinite-dimensional global optimization problem, posed on D, by means of solutions of one-dimensional global optimization problems posed on each curve that densifies D.