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From: "Sarah Wright"
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Subject: real
Date: Tue, 02 Nov 2004 01:59:00 -0500
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X-OriginalArrivalTime: 02 Nov 2004 06:59:01.0392 (UTC) FILETIME=[6EC97900:01C4C0A9]
Status: RO
I was studying for my ph.d qual and I came across that I couldn't solve. I
was
wondering if you wouldn't mind looking at it.
Let {f_n} be a sequence of measurable functions defined on a measurable set
E with finite measure.
Suppose that a family {f_n} is pointwise bounded, that is for each x \in E,
there is a
constant M_x such that |f_n(x)| <= M_x for all n. Show that for all epsilon
>0, there is a closed
set F \subset E with m( E-F) < \epsilon such that the family is uniformly
bounded on F. That
is , show that there is a constant M such that |f_n(x)| <= M for all x \in
F and all n.
Any help you could give would be greatly appreciated.
Thank you for your time
Sarh Wright
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