作者homo3399 (鱼丸)
看板Math
标题[分析] 实变 Royden 里面的习题
时间Mon Dec 27 09:08:51 2010
p79
1.Does the Bounded Convergence Thm hold if m(E)<∞ but we drop the assumption
that the sequence {lfnl} is uniformly bounded on E ?
p89
2.For a measurable function f on [1,∞) which is bounded on bounded sets,
n+1
define an=∫n f for each natural number n
∞
Is it true that f is integrable over [1,∞) iff the series Σn=1 an converge
∞
Is it true that f is integrable over [1,∞) iff the series Σn=1 an
converge absolutely?
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1F：→ doubleN :1.假设 fn 是逐点有界, 用 Egorov's thm 可得 : 12/28 02:29
2F：→ doubleN :对於 ε > 0, 存在一个 E 的闭子集 F 12/28 02:30
3F：→ doubleN :使得 fn 在 F 上均匀有界, 并且 m(E\F) < ε 12/28 02:30
4F：→ doubleN :2.可积分的定义... 12/28 02:32