# Thread: prove countable set is measurable?? plz,

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

plz. help me in that ,,

prove countable setis measurable ???

plz ASAP...

2. ## 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.