Inclusions of Measurable Spaces

Uma Dixit

Assistant Professor, Department of Mathematics, University Post Graduate College, Osmania University, Hyderabad-500003 (Telangana), INDIA.


Let X be a non-empty set, A be a σ - algebra of subsets of X and μ is a positive measure on A so that the triad ( X, A, μ ) is a measure space. The members of the class A are called measurable sets. A measurable function f on X is said to be in Lp (μ ) if ∫􀯑 | 􀝂 |􀯣 􀝀􀟤 < ∞. Lp ( μ ) is a normed linear space for p ≥ 1. L∞ ( μ ) is also a normed linear space. Thus Lp spaces are normed linear spaces for 1 ≤ p ≤ ∞. In this Paper we investigate the conditions under which Lp - spaces will be contained in Lq - spaces where 0 < p < q.

Keywords :

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