[分析] 兩題實分析

[wyob (Go Dolphins)]

作習題的時候卡住了

可能是跳者章節做吧

1.For a measurable function f on [1,∞) which is bounded on bounded sets
             n+1
  defind An=∫  f   for each natural number n
             n
                                                 ∞
 (1)f is integrable over [1,∞) if and only if Σ  An converges  ?
                                                n=1

                                                ∞
 (2)f is integrable over [1,∞) if and only if Σ  An converges absolutely?
                                                n=1





2.Let f be a nonnegative measurable function on R.Show that

      n
 lim ∫ f=∫f
n→∞ -n   R


第二提示要用Fatou lemma嗎?

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