Let n be = (0,1) and 1 < a <∞o. Consider {f} as the sequence of functions such that fn(x) = na e-nx for Vx E S, Vn E N. Show that 1) For any n E N, fn → 0 (strongly converges) pointwise a.e. in 2. -> 2) fn does not strongly converge to 0 in Lº(). 3) {f} is bounded uniformly in La(2), then, there exists M > 0 such that f(n) ≤ M, for VnE N.

Let n be = (0,1) and 1 < a <∞o. Consider {f} as the sequence of functions such that fn(x) = na e-nx for Vx E S, Vn E N. Show that 1) For any n E N, fn → 0 (strongly converges) pointwise a.e. in 2. -> 2) fn does not strongly converge to 0 in Lº(). 3) {f} is bounded uniformly in La(2), then, there exists M > 0 such that f(n) ≤ M, for VnE N.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 74E

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