作习题的时候卡住了 可能是跳者章节做吧 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吗? --

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