Martin-Lof randomness for Bernoulli measures

Continuous maps on Cantor space induce maps between measures on the space. Mauldin has answered the question of when two Bernoulli measures are related by such a map by giving a purely number-theoretic condition on the parameters of the measures. The proof of this result is constructive and hence compatible with algorithmic randomness. We show how Mauldin's result extends to tt-functionals and Martin-L\"of randomness.