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Modern Analysis 2
Homework 03
1. Let
{
f
n
:
n
∈
N
}
be a sequence of functions, each continuous on [
a,b
];
assume that each is continuously diﬀerentiable on (
a,b
). Assume further that
there exist constants
M
0
and
M
1
such that
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Unformatted text preview:  f n ( t )  < M and  f n ( t )  < M 1 for all t ∈ ( a,b ) and all n ∈ N . Prove that some subsequence of { f n : n ∈ N } converges uniformly on [ a,b ]. 1...
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This note was uploaded on 07/08/2011 for the course MAA 5229 taught by Professor Robinson during the Spring '11 term at University of Florida.
 Spring '11
 Robinson

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