77104 20191127155457.0 doi 10.1007/s00224-018-9848-3 sideral 104584 ART-2018-104584 eng (orcid)0000-0002-9109-5337 Mayordomo, E. Universidad de Zaragoza Effective Hausdorff Dimension in General Metric Spaces 2018 Access copy available to the general public Unrestricted We introduce the concept of effective dimension for a wide class of metric spaces whose metric is not necessarily based on a measure. Effective dimension was defined by Lutz (Inf. Comput., 187(1), 49–79, 2003) for Cantor space and has also been extended to Euclidean space. Lutz effectivization uses gambling, in particular the concept of gale and supergale, our extension of Hausdorff dimension to other metric spaces is also based on a supergale characterization of dimension, which in practice avoids an extra quantifier present in the classical definition of dimension that is based on Hausdorff measure and therefore allows effectivization for small time-bounds. We present here the concept of constructive dimension and its characterization in terms of Kolmogorov complexity, for which we extend the concept of Kolmogorov complexity to any metric space defining the Kolmogorov complexity of a point at a certain precision. Further research directions are indicated. info:eu-repo/grantAgreement/ES/MINECO/PSI2014-62092-EXP info:eu-repo/grantAgreement/ES/MINECO/TIN2016-80347-R info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.603 2018 MATHEMATICS 208 / 313 = 0.665 2018 Q3 T3 COMPUTER SCIENCE, THEORY & METHODS 94 / 104 = 0.904 2018 Q4 T3 0.475 2018 Theoretical Computer Science 2018 Q2 Computational Theory and Mathematics 2018 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion 5007 570 Universidad de Zaragoza Dpto. Informát.Ingenie.Sistms. Área Lenguajes y Sistemas Inf. 62, 7 (2018), 1620-1636 Theor. Comput. Syst. THEORY OF COMPUTING SYSTEMS 1432-4350 375984 http://zaguan.unizar.es/record/77104/files/texto_completo.pdf Postprint 54528 http://zaguan.unizar.es/record/77104/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:77104 articulos driver 2019-11-27-15:48:13 ARTICLE