ABSTRACT
In the previous chapter we studied general topological spaces. A topology was defined as a collection of sets (on a carrier) tha t 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 student for another part of analysis - integration. Beyond the familiar integration we experienced in calculus, we will need to measure much more general sets than those which are used for the Riemann integral. For instance, we will consider abstract sets that are encountered in the theory of probability. In addition, we will largely extend the existing class of integrable functions.
