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. 
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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/

[1] M. Deza, T. Deza, Encyclopedia of Distances, Springer, 2009 | MR

[2] P. Grassberger, “Estimating the information content of symbol sequences and efficient codes”, IEEE Trans. Inform. Theory, 35 (1989), 669–675 | DOI | MR

[3] A. Kaltchenko, N. Timofeeva, “Entropy Estimators with Almost Sure Convergence and an $O(n^{-1})$ Variance”, Advances in Mathematics of Communications, 2:1 (2008), 1–13 | DOI | MR | Zbl

[4] A. Kaltchenko, N. Timofeeva, “Rate of convergence of the nearest neighbor entropy estimator”, AEU – International Journal of Electronics and Communications, 64:1 (2010), 75–79 | DOI

[5] E. A. Timofeev, “Statistical Estimation of measure invariants”, St. Petersburg Math. J., 17:3 (2006), 527–551 | DOI | MR | Zbl

[6] E. A. Timofeev, “Bias of a nonparametric entropy estimator for Markov measures”, Journal of Mathematical Sciences, 176:2 (2011), 255–269 | DOI | MR