A simple proof of Debreu’s Gap Lemma

P Ouwehand

Abstract


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.

Full Text:

PDF


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

Refbacks

  • There are currently no refbacks.





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

Powered by OJS and hosted by Stellenbosch University Library and Information Service since 2011.


Disclaimer:

This journal is hosted by the SU LIS on request of the journal owner/editor. The SU LIS takes no responsibility for the content published within this journal, and disclaim all liability arising out of the use of or inability to use the information contained herein. We assume no responsibility, and shall not be liable for any breaches of agreement with other publishers/hosts.

SUNJournals Help