Null sets

Abstract

Abstract In Chapter 9 we introduced null sets as the sets which are negligible in an integration-theoretic sense. On a null set the values of an integrable function f may be altered without changing ∫ f, and on a null set delinquent behaviour is condoned. Certainly any finite set must be null. In general, null sets can be very complicated, reflecting the rich structure of the real line. We do not explore far in this direction, since our emphasis is on functions (modulo their behaviour on negligible sets), rather than on sets per se. The harder sections of this chapter and many of the exercises may without detriment be omitted or delayed.