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How should I show that lim_n ∫〖f_n dm〗 = ∫〖f dm〗?

Jack

New member
Nov 8, 2012
9
Suppose {f_n} is a sequence of functions that converges almost everywhere to a function f
and define F_n = sup_k=1,...n |f_n| .
Show that if the integrals of F_n remain bounded as n goes to infinity,
then lim_n ∫〖f_n dm〗 = ∫〖f dm〗.
 
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CaptainBlack

Well-known member
Jan 26, 2012
890
Suppose {f_n} is a sequence of functions that converges almost everywhere to a function f
and define F_n = sup_k=1,...n |f_n| .
Show that if the integrals of F_n remain bounded as n goes to infinity,
then lim_n ∫〖f_n dm〗 = ∫〖f dm〗.
Please do not copy and paste text with non-standard characters, not everybodies system will render them correctly, learn to use the LaTeX supported here on MHB and on most other maths boards.

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CB
 
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