Question: Let (X, A, ) be a sigma-finite measure space with (X) = . (a) Show that there exists a disjoint sequence (En n N)

Let (X, A, ) be a sigma-finite measure space with (X) =

Let (X, A, ) be a sigma-finite measure space with (X) = . (a) Show that there exists a disjoint sequence (En n N) in A such that UnEN En X and (En) = [1, ) for every n E N. = (b) Show that there exists an extended real-valued measurable function f on X such that f L'(X) and f LP(X) for all p = (1, ].

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