1. Let EC Rd be a measurable set, and 1 p x. Suppose {fn}, {gn} are...
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1. Let EC Rd be a measurable set, and 1 ≤p≤ x. Suppose {fn}, {gn} are two sequences in LP(E). fnf in LP(E), and 9ng in LP(E). Prove: hn= max{fn. 9n} also converges in L"(E). 2. Let EC Rd be a measurable set, and 1 ≤p<q. Prove: (a) If m(E) < x. then L'(E) CLP (E). (b) Is that true L'(R) CLP(R)? Show your argument. 1. Let EC Rd be a measurable set, and 1 ≤p≤ x. Suppose {fn}, {gn} are two sequences in LP(E). fnf in LP(E), and 9ng in LP(E). Prove: hn= max{fn. 9n} also converges in L"(E). 2. Let EC Rd be a measurable set, and 1 ≤p<q. Prove: (a) If m(E) < x. then L'(E) CLP (E). (b) Is that true L'(R) CLP(R)? Show your argument.
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Answer 1 Let EC Rd be a measurable set and 1 p Suppose f g are two sequences in LPE fnf in LPE and g... View the full answer
Related Book For
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
Posted Date:
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