The following theorem appears in Weyl's famous memoir  of 1916.
THEOREM A. Let λ1 ≤ λ2 ≤ … ≤ λn ≤ … be an increasing sequence of positive integers. Suppose that, of the numbers λ1, … λn, the first h1 are equal to each other, then the following h2 and so on, and finally that the last hm coincide. Let hj. If
the sequenceis uniformly distributed (mod 1)for almost all x, in the Lebesgue sense.