Condition on Measure Space Using Sequences

Abstract

The aim of this paper is to present set of condition on measure space space( X, A,  ), where A is a  - algebra of subsets of  X and  is a positive measure on X, for the containment of L^p(μ) in L^q(μ)  where   0 < p < q . We use disjoint sequence {E_n} of  sets  of  positive measure in  and countable number of atoms and give the conditions.