[分析] Royden 習題
Ch2.
18. Let E have finite outer measure. Show that there is an F_sigma set
F and a G_delta set G s.t.
F is included in E, E is included in G, and m*(F)=m*(E)=m*(G).
G_delta部分幾乎跟課本定理證明一樣，所以已經解決，剩下 F_sigma部分。
23. For any set A, define
m***(A) = sup {m*(F) | F is closed and included in A.} .
How is m*** related to m* ?
我認為應該是 m*** = m*，我想本題的關鍵應該與18題我不會做的部分一樣。
目前有做出一個方向：
m***(A) - ε < m*(F) ≦ m*(A) implies m***(A)≦ m*(A).
令一個方向要請教各位高手。
感激不盡！
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 122.117.200.15
推
10/23 22:44, , 1F
10/23 22:44, 1F
推
10/23 22:52, , 2F
10/23 22:52, 2F
推
10/23 23:55, , 3F
10/23 23:55, 3F
推
10/24 00:47, , 4F
10/24 00:47, 4F
推
10/24 00:54, , 5F
10/24 00:54, 5F
推
10/24 02:27, , 6F
10/24 02:27, 6F
→
10/24 08:59, , 7F
10/24 08:59, 7F
→
10/24 09:14, , 8F
10/24 09:14, 8F
→
10/24 09:14, , 9F
10/24 09:14, 9F
→
10/24 09:15, , 10F
10/24 09:15, 10F
推
10/24 19:35, , 11F
10/24 19:35, 11F
→
10/24 19:35, , 12F
10/24 19:35, 12F
→
11/29 21:02, , 13F
11/29 21:02, 13F
討論串 (同標題文章)