Currently working on the task of showing the following: Let $f$ be the Cantor function and $$g: [0,1] \rightarrow [0,1], x \mapsto \frac{f(x)+x}{2}$$
Then $\lambda(g(C)) = \frac{1}{2}$
where $\lambda$ is the Lebesgue measure. I've already shown that $g$ is a homeomorphism and that $\lambda(f(C)) = 1$ but I'm struggling to prove the rest.
Anyone has an idea?