TITLE:
An Elementary Proof That Well-Behaved Utility Functions Exist
AUTHORS:
Mark Voorneveld, Jörgen W. Weibull
KEYWORDS:
Preferences, Utility Theory, Measure Theory, Outer Measure
JOURNAL NAME:
Theoretical Economics Letters,
Vol.6 No.3,
June
6,
2016
ABSTRACT: Starting from an intuitive and constructive approach for countable
domains, and combining this with elementary measure theory, we obtain an upper
semi-continuous utility function based on outer measure. Whenever preferences
over an arbitrary domain can at all be represented by a utility function, our
function does the job. Moreover, whenever the preference domain is endowed with
a topology that makes the preferences upper semi-continuous, so is our utility
function. Although links between utility theory and measure theory have been
pointed out before, to the best of our knowledge, this is the first time that
the present intuitive and straight-forward route has been taken.