6. let (Sa) C Cla, b). Suppose there exsits a function g € Lla, b) with fa(#) S g(x) a.e. for each n. Show that if lim f.(x) f(2) a.e. and h(z) is a bounded measurable function then lim
6. let (Sa) C Cla, b). Suppose there exsits a function g € Lla, b) with fa(#) S g(x) a.e. for each n. Show that if lim f.(x) f(2) a.e. and h(z) is a bounded measurable function then lim
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 15BEXP
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Question
![6. let (S.) cCla, b). Suppose there exsits a function ge Cla, b) with fa(a) S g(x) a.e. for each n. Show
that if
lim f.(z) = f(1) a.e.
and h(z) is a bounded measurable function then
lim
fuh =
fh](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63eaf7d5-11f2-40d7-b6ff-b850261ddc21%2F17551a4c-1ee4-42ca-b4c2-2c796365e676%2Fsg6w7gc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. let (S.) cCla, b). Suppose there exsits a function ge Cla, b) with fa(a) S g(x) a.e. for each n. Show
that if
lim f.(z) = f(1) a.e.
and h(z) is a bounded measurable function then
lim
fuh =
fh
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