Analysis 2Miscellaneous Problems 51. Let (Ω,F, μ) be an arbitrary measure space and let 16p<q<∞. Show thatifp<t<qthenLp(Ω,F, μ)∩ Lq(Ω,F, μ)⊆ Lt(Ω,F, μ).2. LetΩbe an uncountable set andFbe itsσ-algebra of countable or cocountablesubsets. On (Ω,F), letμbe counting measure and letνbe the measure takingvalue 0 on countable sets and 1 on uncountable sets. Show that
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Natural number, Topological space, measure, Countable set, Georg Cantor, arbitrary measure space