is there any countable set which is not measurable? if there is, please help me.
I'm sorry, but I'm sure your question will be answered very swiftly by someone more confident than me!
There are many things you have to define before talking about measurability !
A counterexample is :
Let's deal with , where and is the Lebesgue measure.
The only measurable sets are the ones in .
Hence , which is a countable set, is not measurable !