BV as a dual space.

Let C be a field of subsets of a set I. It is well known that the space FA of all the finitely additive games of bounded variation on C is the norm dual of the space of all simple functions on C. In this paper we prove that the space BV of all the games of bounded variation on C is the norm dual of the space of all simple games on C. This result is equivalent to the compactness of the unit ball in BV with respect to the vague topology.

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Year of publication:	2001-10
Authors:	Maccheroni, Fabio ; Ruckle, William H.
Institutions:	International Centre for Economic Research (ICER)
Subject:	Set functions \| duality \| compactness \| coalitional games

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Extent:	application/pdf
Series:	ICER Working Papers - Applied Mathematics Series.
Type of publication:	Book / Working Paper
Language:	English
Notes:	10 pages
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005135390