Theory of Measure and Integration: Daniell's Version of Lebesgue- Integral

Abstract

Theory of measure and integration involves the consideration of -algebra of subsets of a given space and establish   a specific type of   set function called a measure defied on the -algebra. The integral is defined in terms of a measure of a set. P.J. Daniell gives a direct approach to integration theory as integral is defined as a continuous positive linear functional on a vector lattice. In this paper we here discuss theorems such as Lebesgue Monotone Convergence Theorem, Lebesgue Dominated Convergence Theorem.