m*******s
发帖数: 3142 | 1 For subsets A and B of R, define A+B={a+b|a in A, b in B}
suppose that B is a Borel set, Prove that A+B is a Borel set if A is open
我的思路 大概是 這樣的. 利用 Lindelof定理 ,
A+B= \bigcup_{b\in B}(A+b)=\bigcup_{i=1}^{\infty}(A+{b}_{i}) where {b}_{i}\
in B
再利用Borel set countable union的封閉性,似乎已經完成了證明,里頭根本沒有用到B
is a Borel set. 請問我的 證明是否正確? |
H****h
发帖数: 1037 | 2 A+B is an open set if A is open. So you have nothing to worry about. |
D**u
发帖数: 204 | 3 hahaha, almost got misled by the original question to think about the kind
of stuff like the combination of measurable function and continuous function
...
【在 H****h 的大作中提到】
: A+B is an open set if A is open. So you have nothing to worry about.
|
H*****s
发帖数: 32 | 4 Good point!
【在 H****h 的大作中提到】
: A+B is an open set if A is open. So you have nothing to worry about.
|
m*******s
发帖数: 3142 | 5 這個結論怎么證明呢?
PS: 也就是說我問的那個問題本身給的條件就不太對,是吧?
【在 H****h 的大作中提到】
: A+B is an open set if A is open. So you have nothing to worry about.
|
