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
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Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
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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
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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