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Math Help - prove countable set is measurable?? plz,

  1. #1
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    prove countable set is measurable?? plz,

    plz. help me in that ,,

    prove countable setis measurable ???


    plz ASAP...
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  2. #2
    Super Member girdav's Avatar
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    Re: prove countable set is measurable?? plz,

    Of course it depends of the measured spaces, for example if you take an uncountable set S and the \sigma-algebra given by \{\emptyset,S\} then countable subsets of S need not to be measurable.

    But if you assume for example that (S,\mathcal S) is such that for all x\in S, \{x\}\in\mathcal S then it's just a consequence of the fact that a \sigma-algebra is stable by countable unions.
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