Geodesic
Balls in sequence spaces
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 2, pp. 109-114

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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. 
@article{MAIS_2012_19_2_a7,
     author = {E. A. Timofeev},
     title = {Balls in sequence spaces},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {109--114},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_2_a7/}
}
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E. A. Timofeev. Balls in sequence spaces. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 2, pp. 109-114. http://geodesic.mathdoc.fr/item/MAIS_2012_19_2_a7/