plz. help me in that ,, (Worried)

prove countable setis measurable ??? (Headbang)

plz ASAP...(Crying)

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- Mar 2nd 2012, 01:32 PMazzahprove countable set is measurable?? plz,
plz. help me in that ,, (Worried)

prove countable setis measurable ??? (Headbang)

plz ASAP...(Crying) - Mar 2nd 2012, 02:31 PMgirdavRe: prove countable set is measurable?? plz,
Of course it depends of the measured spaces, for example if you take an uncountable set $\displaystyle S$ and the $\displaystyle \sigma$-algebra given by $\displaystyle \{\emptyset,S\}$ then countable subsets of $\displaystyle S$ need not to be measurable.

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