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HW203 - | f n t |< M and | f n t |< M 1 for all t ∈...

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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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