The Debreu Gap Lemma and some generalizations

DOI10.1016/j.jmateco.2003.06.002zbMath1099.91045OpenAlexW1999871138WikidataQ124852785 ScholiaQ124852785MaRDI QIDQ1886753

Ghanshyam B. Mehta, Gerhard Herden

Publication date: 19 November 2004

Published in: Journal of Mathematical Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmateco.2003.06.002

zbMATH Keywords

Souslin hypothesisCountable chain conditionLexicographically ordered chains

Mathematics Subject Classification ID

Utility theory (91B16)

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Cites Work

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• Ordered topological spaces and the theorems of Debreu and Peleg
• Some results on the existence of utility functions on path connected spaces
• A model of equilibrium with differentiated commodities
• Fundamentals of contemporary set theory
• Debreu's gap theorem
• Utility functions and the order type of the continuum
• Utility theory and continuous monotonic functions
• The non-existence of a utility function and the structure of non-representable preference relations
• Open gaps, metrization and utility
• Ordinal scales in the theory of measurement
• Representations of preference orderings
• Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof.
• Consistency in ordinal data analysis. I.
• On the existence of continuous preference orderings without utility representations
• The foundations of thermodynamics
• Continuity of Preference Relations for Separable Topologies
• Existence of a Continuous Utility Function: An Elementary Proof
• The Utility Theorems of Wold, Debreu, and Arrow-Hahn
• Continuity Properties of Paretian Utility
• Utility and entropy.
• On a theorem of Cooper