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Lambda BV as a Non Separable Dual Space

A. A. Ledari ; Mahdi Hormozi (Institutionen för matematiska vetenskaper)
Iranian Journal of Science and Technology Transaction a-Science (1028-6276). Vol. 34 (2010), A3, p. 237-244.
[Artikel, refereegranskad vetenskaplig]

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).

Nyckelord: Set functions, duality, compactness, non separable

Denna post skapades 2013-01-24. Senast ändrad 2015-07-03.
CPL Pubid: 172067


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