Measurable Spaces and Measurable Functions

Abstract

In the previous chapter we studied general topological spaces. A topology was defined as a collection of sets (on a carrier) that is closed with respect to the formation of arbitrary unions and finite intersections. In the present chapter, we introduce various classes of sets similar to topological spaces but serving other purposes. One of them prepares the reader to another part of analysis, integration. Beyond the familiar integration we experienced in calculus, we need to measure much more general sets than those used for the Riemann integral. For instance, we consider abstract sets that are encountered in the theory of probability. In addition, we largely extend the existing class of integrable functions.