Monatshefte für Mathematik 107(3), 245-256.
ISSN/ISBN: 0026-9255 DOI: 10.1007/BF01300347
Abstract: 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^{3} N 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.
Bibtex:
@article{,
title={On measures of uniformly distributed sequences and Benford's law},
author={Schatte, Peter},
journal={Monatshefte f{\"u}r Mathematik},
volume={107},
number={3},
pages={245--256},
year={1989},
publisher={Springer},
ISSN={0026-9255},
DOI={10.1007/BF01300347},
}
Reference Type: Journal Article
Subject Area(s): Analysis