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Math Help - A quick question on probability measure

  1. #1
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    A quick question on probability measure

    I have read that for a un-contable sample space, not every subset can have a probabiltiy associated to it. (If we do that the axioms of probability measure will get voilated)

    Cosider this
    1. S is un-countable set
    2. Let A be any subset of S. Define P(A) = 1 iff A has a particular element, e0. Else P(A) = 0;

    Doesn't it correctly define a probability measure? And doesn't it define a measure for 'every' subset of S?

    Where am I missing the point? Thanks for any help.
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  2. #2
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    Maybe the theorem you are referring to is that every non-empty subset cannot have a *positive* probability?
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  3. #3
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    Thanks. I am not too sure - I thought what it said was that probability measure can't be difined on the entire power set. It can be defined only on a subset (called sigma algebra). But if 'positive' was impled there then my question is answered. Thanks
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