The integral of the characteristic function is simply the measure of the Smith-Volterra-Cantor Set which is $1/2$. Also any Lebesgue integral function over the Cantor set evaluates to $0$ as the Cantor set is of measure $0$. But what about integrating over the Smith-Volterra-Cantor set which is similar to the Cantor set but has non-zero measure.
I am trying to "approximate" the Smith-Volterra-Cantor Set by closed or open sets and then evaluating the Lebesgue integral over that closed or open set, but not getting the idea. The question is about integrating over "discrete" type of measurable sets (such as the Cantor or the Smith-Volterra-Cantor Set)