Let $\phi$ denote the cantor ternary function and $\mu = \mu_{\phi}$ the associated measure. Let $\lambda$ denote the lebesgue measure. Compute the following integrals.
- $\int_{[0,1]} \phi(t)d\mu (t)$
- $\int_{[0,1]} \phi(t)d \lambda(t)$
- $\int_{[0,1]} td\mu(t)$
I have no clue where to start, any help is appreciated.