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On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process

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Batakis A.

Colloquium Mathematicum

2006

tom 104

nr 2

193-206

We study the Hausdorff dimension of measures whose weight distribution satisfies a Markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the packing dimensions equal the upper Rényi dimensions. As an application we get a continuity property of the Hausdorff dimension of the measures, when viewed as a function of the distributed weights under the $ℓ^{∞}$ norm.

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1 Colloquium Mathematicum

1 Batakis A.

1 2006

Wyniki wyszukiwania

On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process