[分析] 實變 Royden 裡面的習題

看板Math作者 (魚丸)時間15年前 (2010/12/27 09:08), 編輯推噓0(004)
留言4則, 1人參與, 最新討論串1/1
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? -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 115.43.192.87

12/28 02:29, , 1F
1.假設 fn 是逐點有界, 用 Egorov's thm 可得 :
12/28 02:29, 1F

12/28 02:30, , 2F
對於 ε > 0, 存在一個 E 的閉子集 F
12/28 02:30, 2F

12/28 02:30, , 3F
使得 fn 在 F 上均勻有界, 並且 m(E\F) < ε
12/28 02:30, 3F

12/28 02:32, , 4F
2.可積分的定義...
12/28 02:32, 4F
文章代碼(AID): #1D5-ScMm (Math)