Consider the space LP ([0, 1]) where p = (1, ]. (a) Prove that fp is...

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Consider the space LP ([0, 1]) where p = (1, ∞]. (a) Prove that fp is increasing in p for any bounded measurable function f. (b) Prove that ||f||p → f when p→∞0. Consider the space LP ([0, 1]) where p = (1, ∞]. (a) Prove that fp is increasing in p for any bounded measurable function f. (b) Prove that ||f||p → f when p→∞0.

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