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Math Help - das

  1. #1
    Member mabruka's Avatar
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    Jan 2010
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    Mexico City
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    Finite measure property ?

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


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

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


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

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


    \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
    Last edited by mabruka; February 2nd 2010 at 05:37 PM. Reason: Bad title
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  2. #2
    Member mabruka's Avatar
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    Mexico City
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    Turns out the conclusion is wrong! No wonder why i couldnt figure it out!



    it should say

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