[分析] Rudin實變課本32頁的第5題(b)

看板Math作者 (魯丁.嗚嗚溜溜)時間13年前 (2012/09/21 17:16), 編輯推噓1(1推 0噓 6→)
留言7則, 4人參與, 最新討論串1/1
Prove that the set of points at which a sequence of measurable real-valued fun- ctions converges(to a finite limit) is measurable. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.122.140.165
→
09/21 20:25, , 1F
只要會證明，可測函數構成的序列，其limsup和liminf
09/21 20:25, 1F
→
09/21 20:25, , 2F
也可測即可
09/21 20:25, 2F
→
09/21 21:20, , 3F
εδcriterion + {measurable sets} is a σ-algebra
09/21 21:20, 3F
→
09/22 19:15, , 4F
為什麼只要證limsup和liminf也可測就好呢？
09/22 19:15, 4F
推
09/22 19:36, , 5F
因為收斂的點的集合 就是{x:limsup f = liminf f}
09/22 19:36, 5F
→
09/22 19:37, , 6F
現在limsup f 和liminf f都是可測函數
09/22 19:37, 6F
→
09/22 19:38, , 7F
{x:limsup 不等於 liminf}就是可測的
09/22 19:38, 7F
‣ 更多 Rudin5566 的文章
文章代碼(AID): #1GN31pS4 (Math)