Randomness and uniform distribution modulo one (Q2672239)

A sequence \((x_n)_{n\in \omega}\) of reals from \([0,1]\) is uniformly distributed modulo \(1\) if \(\lim_N \frac{|\{n\leq N \mid \{x_n\}\in [a,b)\}|}{N}=b-a\). The authors investigate effective Koksma uniformly distributed reals, i.e. reals \(x\) so that \((u_n(x))\) is uniformly distributed, where \((u_n)_n\) is an effective Koksma sequence. In the paper under review, the authors prove that every Schonrr random real has this property. Some variations of the condition are also considered.