作者keroro321 (日夕)
看板Math
标题[分析] 能否构造出满足以下条件的函数序列
时间Sat Apr 30 11:39:19 2011
Is it possible to construct a sequence {f_i} of continuous functions
such that ( f_i:|R—>|R )
(i) f_i ≧ 0 for all i .
(ii) { x ∣ lim inf f_n(x) = ∞ } = Q ( all rational numbers in |R )
n->∞
先感谢各位板友的回应 !
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1F：→ scan33scan33:R->R ? 04/30 17:57
2F：→ scan33scan33:|R|->R? 04/30 17:57
3F：推 scan33scan33:喔我看懂了，是个粗体orz 抱歉 04/30 18:01
4F：推 scan33scan33:Noㄅ 04/30 18:14
5F：推 scan33scan33:ㄟ？是inf唷？...那要想一下 04/30 18:17
6F：推 scan33scan33:用一堆Dirac Delta function? 04/30 18:30
7F：→ scan33scan33:先做{x | lim inf f_n(x) = inf} = N 04/30 18:31
8F：→ scan33scan33:令 f_n = \sum_{i=1}^n delta(i) 04/30 18:32
9F：→ scan33scan33:会有以上结果，然後因为Q可数，故可以类似得证？ 04/30 18:32
10F：推 scan33scan33:无理数还是太蜜了...无限和可能会lose...再想看看好 04/30 18:40