NJ
发帖数: 44 | 1 举个例子使得measure of the Union of Ei小于measure of Ei的和。
其中是disjoint sequence
多谢了 |
NJ
发帖数: 44 | 2 Any mutually disjoint sequence. Thanks. |
z****f
发帖数: 484 | 3 Banach-Tarski theorem？
【在 NJ 的大作中提到】
: Any mutually disjoint sequence. Thanks.
|
z****f
发帖数: 484 | |
z****f
发帖数: 484 | |
H****h
发帖数: 1037 | 6 说measure of E就隐含了E是可测集合的意思。
【在 z****f 的大作中提到】
: 你看后面的回帖
|
j******w
发帖数: 690 | 7 no
Here is just a hint:
If \Sum_i \mu(E_i)<\infty, then the index set of positive measure sets must
be countable.
Here I just simply assume ``the sum" is the least upper bound of all
countable sums.
Actually one can show that there exists no uncountably many mutually
disjoint positive measure sets.
【在 NJ 的大作中提到】
: 举个例子使得measure of the Union of Ei小于measure of Ei的和。
: 其中是disjoint sequence
: 多谢了
|
