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:
@article{1632,
title = {Simplification and Strengthening of Weyl's Definition of Asymptotic Equal Distribution of Two Families of Finite Sets},
journal = {CUBO, A Mathematical Journal},
volume = {6},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/1632}
}
Trench, William F. Simplification and Strengthening of Weyl's Definition of Asymptotic Equal Distribution of Two Families of Finite Sets. CUBO, A Mathematical Journal, Tome 6 (2004) 8 p. http://gdmltest.u-ga.fr/item/1632/