Geometric discrepancy theory and uniform distribution

John Ralph Alexander, József Beck, William W.L. Chen

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations

Abstract

A sequence s 1, s 2, … $ s_1, s_2,\ldots $ in U = [ 0, 1) $ { \text{ U}}=[0,1) $ is said to be uniformly distributed if, in the limit, the number of s j $ s_j $ falling in any given subinterval is proportional to its length. Equivalently, s 1, s 2, … $ s_1, s_2,\ldots $ is uniformly distributed if the sequence of equiweighted atomic probability measures µ N (s j) = 1 / N $ \mu _N(s_j)=1/N $, supported by the initial N-segments s 1, s 2, …, s N $ s_1, s_2,\ldots, s_N $, converges weakly to Lebesgue measure on U $ {{ \text{ U}}} $. This notion immediately generalizes to any topological space with a corresponding probability measure on the Borel sets.

Original languageEnglish (US)
Title of host publicationHandbook of Discrete and Computational Geometry, Third Edition
PublisherCRC Press
Pages331-357
Number of pages27
ISBN (Electronic)9781498711425
ISBN (Print)9781498711395
DOIs
StatePublished - Jan 1 2017

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Geometric discrepancy theory and uniform distribution'. Together they form a unique fingerprint.

Cite this