bv as a non separable dual space

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.