Hi!

Can any one make this a little bit more clear please?

Let $\displaystyle ( E, p ) $ be a metric space, and $\displaystyle P:\mathcal B(E)\longrightarrow \mathbb{R}_+$ a probability measure on borel sets of E.

I do not understand the next implication: $\displaystyle x \in E, \epsilon >0$

Since $\displaystyle \delta (B_\epsilon (x)) \subset \{y \in E : p(x,y)=\epsilon \} $

then

$\displaystyle P( B_\epsilon (x))= 0$ for (at most) a numerable number of $\displaystyle \epsilon$

$\displaystyle \delta (B_\epsilon (x))$ is the topological boundary

I think i may be missing a "core" property of finite measures but i dont remember!

Thanx in advance

EDIT: Bad title i can't fix this sorry