A CATEGORICAL APPROACH TO INTEGRAL OF MEASURES AND DISINTEGRATION OF MEASURES

Abstract

We introduce the notions of universal integral, conditional expectation and universal disintegration, using exclusively category theory. By these notions we approach the corresponding measure-theoretic ones, and we give new tools to study the existence problems of disintegrations and strong liftings. Furthermore, we prove in an easy way some theorems which one can find in the excellent work of L. Schwartz in [19].