  We elaborate the notions of Martin-L\"of and Schnorr randomness for real
numbers in terms of uniform distribution of sequences. We give a necessary
condition for a real number to be Schnorr random expressed in terms of
classical uniform distribution of sequences. This extends the result proved by
Avigad for sequences of linear functions with integer coefficients to the wider
classical class of Koksma sequences of functions. And, by requiring
equidistribution with respect to every computably enumerable open set
(respectively, computably enumerable open set with computable measure) in the
unit interval, we give a sufficient condition for Martin-L\"of (respectively
Schnorr) randomness.
