The Debreu Gap Lemma and some generalizations

The Debreu Gap Lemma and some generalizations

In this paper we study the Debreu Gap Lemma and its generalizations to totally ordered sets more general than ( R,≤) . We explain why it is important in economics to study utility functions which may not be real-valued and we build the foundations of a theory of continuity of such generalized utilit...

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Veröffentlicht in:Journal of mathematical economics 2004-11, Vol.40 (7), p.747-769
Hauptverfasser: Herden, G., Mehta, G.B.
Format: Artikel
Sprache:eng
Schlagworte:
Countable chain condition
Debreu Gap Lemma
Economic analysis
Economic theory
Hypothesis
Lexicographically ordered chains
Mathematical methods
Mathematical models
Souslin hypothesis
Studies
Utility functions
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Zusammenfassung:In this paper we study the Debreu Gap Lemma and its generalizations to totally ordered sets more general than ( R,≤) . We explain why it is important in economics to study utility functions which may not be real-valued and we build the foundations of a theory of continuity of such generalized utility functions.
ISSN:0304-4068
1873-1538
DOI:10.1016/j.jmateco.2003.06.002