Simplification and Strengthening of Weyl's Definition of Asymptotic Equal Distribution of Two Families of Finite Sets

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Abstract

Suppose that -∞ < a < b < ∞, a ≤ u1n â‰¤ u2n â‰¤ . . . â‰¤ unn â‰¤ b, and a â‰¤ v1n â‰¤ v2n â‰¤ . . . â‰¤ vnn â‰¤ 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:

 

Keywords

asymptotic equal distribution
  • William F. Trench 95 Pine Lane, Woodland Park, CO 80863 USA Trinity University, San Antonio, Texas, USA.
  • Pages: 47-54
  • Date Published: 2004-10-01
  • Vol. 6 No. 3 (2004): CUBO, A Mathematical Journal

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Published

2004-10-01

How to Cite

[1]
W. F. Trench, “Simplification and Strengthening of Weyl’s Definition of Asymptotic Equal Distribution of Two Families of Finite Sets”, CUBO, vol. 6, no. 3, pp. 47–54, Oct. 2004.

Issue

Vol. 6 No. 3 (2004): CUBO, A Mathematical Journal

Section

Articles