3. Let {gn} be a sequence of integrable functions such that gn → g a.e. with g integrable. Show that lim fgn – g| = 0 if and only if lim f [gn| = S \g] .
3. Let {gn} be a sequence of integrable functions such that gn → g a.e. with g integrable. Show that lim fgn – g| = 0 if and only if lim f [gn| = S \g] .
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 fgng be a sequence of integrable functions such that gn ! g
a.e. with g integrable. Show that lim jgn
![3. Let {gn} be a sequence of integrable functions such that gn → g
a.e. with g integrable. Show that lim f\gn - g| = 0 if and only if
lim f \gn| = S \g] .
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Transcribed Image Text:3. Let {gn} be a sequence of integrable functions such that gn → g
a.e. with g integrable. Show that lim f\gn - g| = 0 if and only if
lim f \gn| = S \g] .
n-00
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