Mathematical Analysis
A Billingsley type theorem for Bowen entropy
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 503-507.

For subsets of a metric space with a continuous map, Bowen introduced a notion of entropy. In this Note we show that the Bowen entropy can be determined via the local entropies of measures. This result can be considered as an analogue of Billingsley's Theorem for the Hausdorff dimension.

Pour les sous-ensembles d'un espace métrique muni d'une application continue, Bowen avait introduit une notion d'entropie. Dans cette Note nous démontrons que l'entropie de Bowen peut être déterminée par les entropies locales de mesures. Ce résultat est un analogue du théorème de Billingsley pour la dimension de Hausdorff.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2008.03.010
Ma, Ji-Hua 1; Wen, Zhi-Ying 2

1 Department of Mathematics, Wuhan University, Wuhan 430072, PR China
2 Department of Mathematics, Tsinghua University, Beijing 100081, PR China
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Ma, Ji-Hua; Wen, Zhi-Ying. A Billingsley type theorem for Bowen entropy. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 503-507. doi : 10.1016/j.crma.2008.03.010. http://www.numdam.org/articles/10.1016/j.crma.2008.03.010/

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[4] Federer, H. Geometric Measure Theory, Springer-Verlag, New York, 1969

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[7] Pfister, C.E.; Sullivan, W.G. On the topological entropy of saturated sets, Ergodic Theory Dynam. Systems, Volume 27 (2007), pp. 929-956

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