Lambda BV as a Non Separable Dual Space
Artikel i vetenskaplig tidskrift, 2010

Let C be a field of subsets of a set I. Also, let Lambda = {lambda(i)}(i=1)(infinity) be a non-decreasing positive sequence of real numbers such that lambda(1) = 1, 1/lambda(i) -> 0 and Sigma(infinity)(i=1) 1/lambda(i) = infinity. In this paper we prove that Lambda BV of all the games of Lambda-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 Lambda 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).

duality

Set functions

non separable

compactness

Författare

A. A. Ledari

Mahdi Hormozi

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Iranian Journal of Science and Technology, Transaction A: Science

1028-6276 (ISSN)

Vol. 34 A3 237-244

Ämneskategorier

Matematik