BV AS A NON SEPARABLE DUAL SPACE

Abstract

Let C be a field of subsets of a set I. Also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . In this paper we prove thatBV of all the games of -bounded variation on C is a non-separable and norm dual Banach space of thespace of simple games on C . We use this fact to establish the existence of a linear mapping T from BVonto F A (finitely additive set functions) which is positive, efficient and satisfies a weak form of symmetry,namely invariance under a semigroup of automorphisms of I,C.