Question
For each n N, let fn be a function defifined on [0 , 1]. Prove that if ( fn ) is bounded on [0 ,
For each n N, let fn be a function defifined on [0, 1]. Prove that if (fn) is bounded on [0, 1] and if (fn) is equi-continuous, then (fn) contains a uniformly convergent subsequence.
It's Arzela-Ascoli Theorem.
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Algebra 1, Volume 2
Authors: Edward B. Burger, Juli K. Dixon, Steven J. Leinwand, Timothy D. Kanold
Student Edition
0544368185, 978-0544368187
