3) Let fn(x) = X-n,n] (x), for x E R. Find the pointwise limit J of (Jn)n and now that a) the pointwise convergence does not imply the convergence in measure, b) the convergence in mean does not imply the convergence in measure. c) the convergence in mean does not imply the absolute convergence in mean.
3) Let fn(x) = X-n,n] (x), for x E R. Find the pointwise limit J of (Jn)n and now that a) the pointwise convergence does not imply the convergence in measure, b) the convergence in mean does not imply the convergence in measure. c) the convergence in mean does not imply the absolute convergence in mean.
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 72E
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![(3) Let fn(x) = X[-n,n] (x), for x € R. Find the pointwise limit f of (fn)n and
show that
(a) the pointwise convergence does not imply the convergence in measure,
(b) the convergence in mean does not imply the convergence in measure.
(c) the convergence in mean does not imply the absolute convergence in mean.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ee1dac4-3c1a-4c0f-b49c-2cac8372fdf5%2Fcf6f8dd5-86fb-4aef-b132-b411fb4af1a9%2Fq4rbho_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(3) Let fn(x) = X[-n,n] (x), for x € R. Find the pointwise limit f of (fn)n and
show that
(a) the pointwise convergence does not imply the convergence in measure,
(b) the convergence in mean does not imply the convergence in measure.
(c) the convergence in mean does not imply the absolute convergence in mean.
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