Given $A,B$ u.d. in [0,1] and $k\in\mathbb{N}$ we define $X:=A+kB-\{A+kB\}$. How to prove $X$ is u.d..
I read something about the "Weyl equidistribution theorem" (by google). But I never heard sth about ergodic theory before. I wonder if there is literature or an easy proof for the statement above. I try to show it directly with cdf. This statement is a generalization of an exercise in "Morgan, B.J.T., Elements of Simulation" (p.72).
$\{\bullet\}$ means the largest integer