Specic Complete Measure in the Structure of a Utility Function

In this article, an outer measure is constructed on a pseudo- ordered set (X;%) and then it will be shown that it is in fact a measure dened on the whole power set of X . Applying this, a measurable utility function is dened which represents the relation % on X. Also, we discuss the continuity and upper semi-continuity of in certain points of X. Finally, the results are used to improve some of the theorems in economics.