plz. help me in that ,,
prove countable setis measurable ???
plz ASAP...
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.