Suppose that -∞ < a < b < ∞, a ≤ u1n ≤ u2n ≤ . . . ≤ unn ≤ b, and a ≤ v1n ≤ v2n ≤ . . . ≤ vnn ≤ b, n ≥ 1. We simplify and strenghthen Weyl's definition of asymptotic equal distribution of U = {{uin}ni=1}n≥1 and V = {{vin}ni=1}n≥1 by showing that the following statements are equivalent: