Compactifications and Problems of Integration

Abstract

In this chapter we continue to consider the effects arising when employing extensions in the class of FAM. But we now discuss some applications of extensions to problems of ‘pure’ mathematics. We investigate the problems of universal integrability of bounded functions and universal measurability of sets. In these questions the effects of cornpactifications in the class of FAM are also presented. Of course, here we strive to attain other goals. We pay the basic attention to corresponding constructions of functional analysis. However, in the most essential questions the constructions considered below have much in common with constructions of the applied character given in the previous chapters.