[分析] 能否構造出滿足以下條件的函數序列

[keroro321 (日夕)]

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->∞

先感謝各位板友的回應 !

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→ scan33scan33:R->R ?
→ scan33scan33:|R|->R?
推 scan33scan33:喔我看懂了，是個粗體orz 抱歉
推 scan33scan33:Noㄅ
推 scan33scan33:ㄟ？是inf唷？...那要想一下
推 scan33scan33:用一堆Dirac Delta function?
→ scan33scan33:先做{x | lim inf f_n(x) = inf} = N
→ scan33scan33:令 f_n = \sum_{i=1}^n delta(i)
→ scan33scan33:會有以上結果，然後因為Q可數，故可以類似得證？
推 scan33scan33:無理數還是太蜜了...無限和可能會lose...再想看看好