i couldn't find a way to show this function is measurable.

$\displaystyle f(x)=1$ if $\displaystyle x \epsilon F $ and $\displaystyle f(x)=sin(x)$ if $\displaystyle x\varepsilon [0,1]\F $ where F is the Cantor Set.

i will be appreciate for any help.

edit: i defined a function $\displaystyle g(x)=sin(x)$ over the interval [0,1] but i am not sure about $\displaystyle f \approx g $ because f takes value 1 for some points in [0,1] so there will be discontinuity