作者GSXSP (Gloria)
看板Math
標題[分析] bounded vs. convergent subsequence
時間Sat Jul 9 08:04:05 2016
Q1:
f_k (i) uniformly bounded for all i = 1, 2 ,...
Can we find a subsequence k_j such that
f_{k_j} (i) converge for all i=1,2,...
Q2:
f_k(x) uniformly bounded for all x \in [0,1]
Can we find a subsequence k_j such that
f_{k_j} (x) converge for all x \in [0,1]
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→ kerwinhui : No&No, unless you impose more constraints on f_k 07/09 15:30
→ GSXSP : counter-example? 07/10 01:27