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It's a well known theorem, that given it's outer measure is finite, a set is measurable if and only if it's outer and inner measure are equal. So i need a justification of the assumption of the outer measure of the set being finite, i.e.,(may be) an example of a non measurable set with both it's outer and inner measure infinite...

thanks in advance, and it's a homework problem...

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up vote 3 down vote accepted

Hint: If $A \subseteq [0,1]$, what is the inner and outer measure of $( - \infty , 0 ) \cup A \cup ( 1 , + \infty )$?

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thanks a lot....got it...:) –  aranya Jan 27 '13 at 6:50

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