Some important theorems in measure theory

Abstract

In this monograph I shall give several important theorems in measure theory which are not included in any regular graduate/undergraduate courses in measure theory nor are they normally included in standard text books in measure theory. All these theorems are important and have several applications. I shall assume that you know some set theory, some Boolean algebras and some functional analysis. You should definitely know some basic measure theory. Since my aim is to make you familiar with these theorems and their proofs I make no attempt to give the most general versions. Instead, I confine myself to the simplest possible versions without losing the beauty of the proofs.