※ 引述《Pacers31 (17)》之銘言：
: Give an example that Hahn decomposition is not unique.
: 除了證明裡提到的那個分解外，實在想不到不唯一的例子
最簡單的例子：
X = {0} with the σ-algebra of all subsets of X
and signed measure υ(A) = ΣA = 0.
Decomposition 1: P = {0}, N = { }
Decomposition 2: P = { }, N = {0}
In general, null sets can be transferred from P to N
or from N to P, and the result would be another
Hahn decomposition of X.
In the example above, {0} was an example of a null set.
: 另外似乎有這個性質
: 若對於全空間X，存在有兩組Hahn decomposition
: X=A∪B , X=C∪D (A,C is positive , B,D is negative 關於 sign measureμ)
: 則μ(A∩E)=μ(C∩E), μ(B∩E)=μ(D∩E) for all E contain in X
: 不知道是不是能從這個性質出發去想分解不唯一的例子?
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 75.62.128.123
※ 編輯: cgkm 來自: 75.62.128.123 (10/18 01:36)
※ 編輯: cgkm 來自: 75.62.128.123 (10/18 01:38)