The Interplay Between Measure Theory and Topology

Abstract

A connection between measure theory and topology is established when a eld F is de ned in terms of topological properties. More precisely, we de ned F as the smallest eld containing all the open sets of a topological space , then there are interesting interrelation between measure theory and topology. We study the interrelation between topological space, open sets and continuous functions in one hand and measure space, measurable set and measurable function on the other.