1. Let (X, M, µ) be a measure space, fn : X → [0, 1] a sequence of measurable func- tions. Show that the set {x: lim fn(x) exists } C X n 00 is measurable.
1. Let (X, M, µ) be a measure space, fn : X → [0, 1] a sequence of measurable func- tions. Show that the set {x: lim fn(x) exists } C X n 00 is measurable.
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, M, µ) be a measure space, fn : X → [0, 1] a sequence of measurable func-
tions. Show that the set
{x: lim fn(x) exists } C X
n 00
is measurable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6067f2cc-68b3-4db6-902b-1d11d6726e7b%2F35179f9f-3525-4410-b3e8-e842b83eb6db%2Fru7dy6_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let (X, M, µ) be a measure space, fn : X → [0, 1] a sequence of measurable func-
tions. Show that the set
{x: lim fn(x) exists } C X
n 00
is measurable.
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