Almost measurable real-valued functions

Abstract

In this chapter the notion of an almost measurable real-valued function is introduced and examined. Some properties of such functions are considered and their characterization is given by using the classical Fubini theorem and a theorem on the existence of measurable selectors (see Appendix 2). In addition to this result, close connections of almost measurable functions with extensions of the standard Lebesgue measure on the real line are pointed out and the structure of algebraic sums of almost measurable functions is studied.