The characteristic Function of SVC, $ \chi$ is not Riemann integrable as proved here But it can be shown that $ \chi $ is Lebesgue integrable. $ $ \int_0^1 \chi d\mu=\int_{SVC} \chi d\mu+\int_{[0,1]\setminus {SVC}} \chi d\mu=\int_{SVC} d\mu=\mu(SVC)=\frac{1}{2}.$ $ Question 1:- Is this correct? Now to prove $ \chi$ is HK- integrable, Let $ \epsilon>0$ beRead more