  We prove various results on effective numberings and Friedberg numberings of
families related to algorithmic randomness. The family of all Martin-L\"of
random left-computably enumerable reals has a Friedberg numbering, as does the
family of all $\Pi^0_1$ classes of positive measure. On the other hand, the
$\Pi^0_1$ classes contained in the Martin-L\"of random reals do not even have
an effective numbering, nor do the left-c.e. reals satisfying a fixed
randomness constant. For $\Pi^0_1$ classes contained in the class of reals
satisfying a fixed randomness constant, we prove that at least an effective
numbering exists.
