Regular economies and sets of measure zero in Banach spaces
type: Item
instance of: scholarly article
title: Regular economies and sets of measure zero in Banach spaces
zbMATH Open document ID: 0582.90013
DOI: 10.1016/0304-4068(85)90028-X
author: Aloisio Araujo
published in: Journal of Mathematical Economics
publication date: 1985-01-01T00:00:00Z
review text: Debreu had shown that for economies described by initial endowments the set of non-regular economies forms a closed set of Lebesgue measure zero. In the present paper the same result is considered when economies are described by both initial endowments and utility functions. Since there is no analogue of Lebesgue measure in infinitely dimensional spaces, several alternative concepts of measure zero are considered and it is shown that for some of them the Debreu result holds even if economies are described by endowments and utility functions.
Mathematics Subject Classification ID: 91B50
zbMATH DE Number: 3932732
zbMATH Keywords: non-regular economies
zbMATH Keywords: closed set of Lebesgue measure zero
zbMATH Keywords: infinitely dimensional spaces
reviewed by: Anjan Mukherji
MaRDI profile type: Publication
cites work: Differentiability of Lipschitzian mappings between Banach spaces
cites work: Q5583383
cites work: Borel Structures in Groups and Semigroups.
cites work: Economies with a Finite Set of Equilibria
cites work: Topological methods in Walrasian economics
cites work: Gaussian null sets and differentiability of Lipschitz map on Banach spaces
cites work: Global analysis and economics. II: Extension of a theorem of Debreu
full work available at URL: 0304-4068(85)90028-x
OpenAlex ID: W2029867979
description: scientific article; zbMATH DE number 3932732