Combinatorial properties of the Hausdorff dimension. (English) Zbl 0709.11041

The author considers subsets F of \(X^{\omega}\), the space of infinite sequences over an alphabet of cardinality r. Introducing a suitable entropy \(H_ F\) for such sets (in terms of combinatorial properties) he shows that, for a certain class of such sets, \(H_ F\) equals the Hausdorff dimension of the set obtained by interpreting each \(x\in F\) as the base r expansion of a real number.
Reviewer: B.Volkmann


11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
68Q45 Formal languages and automata
94A17 Measures of information, entropy
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