Abstract
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 ω-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.
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This work was supported by the Natural Science and Engineering Research Council of Canada, Grant OGP0000243.
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Jürgensen, H., Staiger, L. Local Hausdorff dimension. Acta Informatica 32, 491–507 (1995). https://doi.org/10.1007/BF01213081
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DOI: https://doi.org/10.1007/BF01213081