Balls in sequence spaces

E. A. Timofeev

P. G. Demidov Yaroslavl State University

Abstract: We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. For example, the measure of a ball is discontinuous at every binary rational value of $\log r$, where $r$ is the radius.

Keywords: entropy, nonparametric statistic, ball, Bernoulli's measure.

UDC: 519.987

Received: 14.01.2012