Randomness and uniform distribution modulo one

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