1. Let (X, µ) be any measure space, and let p > 0. Prove that if | fn-fp0 and sup,, ||fn|lp ≤ M, then ||f||, M.Hint: You'll have to treat the cases 1≤p≤0 and 0

It is given that X be any measure space, p > 0. Objective: To prove that if ||fn-f||p→0 and…

Answered: 1. Let (X,) be any measure space, and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Let (X,) be any measure space, and let p > 0. Prove that if fn-fp0 and sup,, ||fn|lp SM, then || SM.