10 (a) Suppose (X, S, ) is a measure space such that (X) < . Suppose...

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10 (a) Suppose (X, S, μ) is a measure space such that µ(X) < ∞. Suppose p,r are positive numbers with p < r. Prove that if f: X → [0, ∞) is an S-measurable function such that ff" du <∞, then f f dμ <∞. (b) Give an example to show that the result in part (a) can be false without the hypothesis that (X) < ∞. 10 (a) Suppose (X, S, μ) is a measure space such that µ(X) < ∞. Suppose p,r are positive numbers with p < r. Prove that if f: X → [0, ∞) is an S-measurable function such that ff" du <∞, then f f dμ <∞. (b) Give an example to show that the result in part (a) can be false without the hypothesis that (X) < ∞.

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a Let f be the derivative ... View the full answer