[分析] 兩題實分析
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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