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.
