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.
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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![(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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