On a Theorem of Weyl,

Abstract

If A is a Lebesque measurable subset of the interval (0,1) and t is any irrational number in that interval, then by a well-known theorem of Weyl, the frequency with which the integer products of t modulo one fall in A converges to the measure of A. This result may be used to evaluate asymptotic error in certain approximations. For a special case, Weyl's theorem is shown to extend to rational numbers t and a lower bound on frequency is derived. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1971
Accession Number
AD0722381

Entities

People

  • Warren F. Rogers

Organizations

  • Center for Naval Analyses

Tags

DTIC Thesaurus Topics

  • Frequency
  • Intervals
  • Irrational Numbers
  • Numbers
  • Rational Numbers

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.