On Measurable Sets

Abstract

Caratheodory's axiomatic approach to the theory of measure is well known. It consists in starting with an outer measure m*, a set function defined axiomatically on the class of all subsets of a given set X, and singling out a particular class of subsets of X, called the outer measurable sets, in such a way that the restriction of m* to this distinguished subclass is well-behaved.