Some density properties of the closed unit ball of

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 D , by means of solutions of one-dimensional global optimization problems posed on each curve that densifies D .