(2) Let fn(x) = X(0,n)(x), x > 0. Find the pointwise limit f of (fn)n and show that (a) the pointwise convergence does not imply the convergence in mean, (b) the pointwise convergence does not imply the absolute convergence in

(2) Let fn(x) = X(0,n)(x), x > 0. Find the pointwise limit f of (fn)n and show that (a) the pointwise convergence does not imply the convergence in mean, (b) the pointwise convergence does not imply the absolute convergence in

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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Question

(2) Let fn(x) = X(0,n)(x), x > 0. Find the pointwise limit f of (fn)n and
show that
(a) the pointwise convergence does not imply the convergence in mean,
(b) the pointwise convergence does not imply the absolute convergence in
mean.

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