Effective dimension in some general metric spaces

Elvira Mayordomo

We introduce the concept of effective dimension for a general metric space. Effective dimension was defined by Lutz in (Lutz 2003) for Cantor space and has also been extended to Euclidean space. Our extension to other metric spaces is based on a supergale characterization of Hausdorff dimension. We present here the concept of constructive dimension and its characterization in terms of Kolmogorov complexity. Further research directions are indicated.

In Benedikt Löwe and Glynn Winskel: Proceedings 8th International Workshop on Developments in Computational Models (DCM 2012), Cambridge, United Kingdom, 17 June 2012, Electronic Proceedings in Theoretical Computer Science 143, pp. 67–75.
Published: 29th March 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.143.6 bibtex PDF
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