Zentralblatt für Mathematik
Mathematics Abstracts

Juergensen, H.; Staiger, L. :
Local Hausdorff dimension. ( English )
Acta Inf. 32, No.5, 491-507 (1995).

Classification

*68Q30 Algorithmic information theory

Keywords

closed $\omega$-languages; local Kolmogorov complexity

We define the notion of local size-measure in metric spaces and derive general properties of local size-measures. Special cases include the local Hausdorff dimension, the local entropy, and the local Kolmogorov complexity. For the case of finite-state and closed $\omega$-languages we exhibit an algorithm for the approximate calculation of the local Hausdorff dimension using the fact that, in this case, the local Hausdorff dimension and the local entropy coincide.

Publ. Year: 1995
Document Type: J