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Schatte, P (1989)

On measures of uniformly distributed sequences and Benford's law

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 log3 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.

@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