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Unformatted text preview: δ := ±/M we get that  ts  < δ implies  f n ( t )f n ( s )  <  ts  M < δM < ( ±/M ) M = ± . (c) All the assumptions of Theorem 7.25 in Rudin are satisﬁed. The sequence of f n ’s are deﬁned on the compact set [0 , 1], they are uniformly bounded from part (a) and thus pointwise bounded, and they are equiconintuous from part (b); thus, some { f n k } converges to some f , uniformly on [0 , 1]. ± 1...
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This note was uploaded on 12/20/2011 for the course MATHEMATIC 201 taught by Professor Joshuamiller during the Spring '11 term at Fudan University.
 Spring '11
 JoshuaMiller
 Math

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