Balls in Sequence Spaces

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

• энтропия
• непараметрическая оценка
• шар
• мера Бернулли