  Algorithmic learning theory traditionally studies the learnability of
effective infinite binary sequences (reals), while recent work by [Vitanyi and
Chater, 2017] and [Bienvenu et al., 2014] has adapted this framework to the
study of learnability of effective probability distributions from random data.
We prove that for certain families of probability measures that are
parametrized by reals, learnability of a subclass of probability measures is
equivalent to learnability of the class of the corresponding real parameters.
This equivalence allows to transfer results from classical algorithmic theory
to learning theory of probability measures. We present a number of such
applications, providing many new results regarding EX and BC learnability of
classes of measures, thus drawing parallels between the two learning theories.
