BV AS A NON SEPARABLE DUAL SPACE

Document Type: Regular Paper

Authors

1 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, I. R. of Iran

2 University of Gothenburg, Chalmers University of Technology, Gotheburg, Sweden

Abstract

Let C be a field of subsets of a set I. Also, let  
   1 i i
 be a non-decreasing positive
sequence 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 the
space of simple games on C . We use this fact to establish the existence of a linear mapping T from BV
onto 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.

Keywords