Convergence On Daniell Space With Some Of Their Properties

Abstract

In this work, we introduce the concept of three types of convergence (convergence almost everywhere, almost uniformly convergence, convergence in norm) in relation to Daniell integration with the properties of each type, and then discuss the relationship between these three types, and finally we present the basic theorems of convergence, such as Dominated convergence theorem, monotone convergence theorem and Fatou's lemma