Specific Complete Measure in the Structure of a Utility Function

Abstract

An outer measure is constructed on a pseudo-ordered set(X,≿) and then it will be shown that it is in fact a measure defined onthe whole power set of X . Applying this, a measurable utility functionθ is defined which represents the relation ≿ on X. Also, we discuss thecontinuity and upper semi-continuity of θ in certain points of X. Finally,the results are used to improve some of the theorems in economics.