[機統] Durret 習題
Durret 第四版的1.3.8 和1.3.9
1.3.8
Use the previous exercise to conclude that Y is measurable w.r.t σ(X)
iff Y = f(X) where f:R -> R is measurable
1.3.9
To get a constructive proof of the last result, note that
{ω: m2^-n ≦ Y ＜ (m+1)2^-n } = {X 屬於 Bm,n} for some Borel set Bm,n
and set fn(x) = m2^-n for x 屬於 Bm,n and show that as n -> ∞ and
Y = f(X)
1.3.8只會證明出有 f: X(Ω) -> R
1.3.9 不懂為什麼 固定n , Bm,n 會形成對R的partition
假如 Bm,n 之間 交集非空，那fn不就無法定義了嗎?
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.113.127.204
※ 編輯: c76068 來自: 140.113.127.204 (03/18 22:00)
→
03/19 09:12, , 1F
03/19 09:12, 1F
→
03/19 22:26, , 2F
03/19 22:26, 2F
→
03/19 22:30, , 3F
03/19 22:30, 3F