A simple proof of Debreu’s Gap Lemma

P Ouwehand


Debreu’s Gap Lemma is central to the proof of his fundamental result on the existence of continuous utility functions. A short proof based on a standard textbook construction of utility functions on countable linearly ordered sets is presented here. The proof is accessible to students with limited mathematical background, thus making it suitable for inclusion in elementary texts on utility theory.

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DOI: https://doi.org/10.5784/26-1-83


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ISSN 2224-0004 (online); ISSN 0259-191X (print)

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