On measures of uniformly distributed sequences and Benford's law
type: Item
instance of: scholarly article
title: On measures of uniformly distributed sequences and Benford's law
zbMATH Open document ID: 0678.10036
DOI: 10.1007/BF01300347
author: Peter Schatte
published in: Monatshefte für Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178425
review text: The metric theory of uniform distribution of sequences is complemented by considering product measures with not necessarily identical factors. A necessary and sufficient condition is given under which a general product measure assigns the value one to the set of uniformly distributed sequences. For a stationary random product measure, almost all sequences are uniformly distributed with probability one. The discrepancy is estimated by \(N^{-1/2}\log^ 3N\) for sufficiently large N. Thus the metric predominance of uniformly distributed sequences is stated, and a further explanation for Benford's law is provided. The results can also be interpreted as estimates of the empirical distribution function for non-identical distributed samples.
reviewed by: Peter Schatte
Mathematics Subject Classification ID: 11K06
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 4110803
zbMATH Keywords: uniform distribution of sequences
zbMATH Keywords: product measures
zbMATH Keywords: stationary random product measure
zbMATH Keywords: discrepancy
zbMATH Keywords: Benford's law
zbMATH Keywords: empirical distribution function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4110803