000077104 001__ 77104 000077104 005__ 20191127155457.0 000077104 0247_ $$2doi$$a10.1007/s00224-018-9848-3 000077104 0248_ $$2sideral$$a104584 000077104 037__ $$aART-2018-104584 000077104 041__ $$aeng 000077104 100__ $$0(orcid)0000-0002-9109-5337$$aMayordomo, E.$$uUniversidad de Zaragoza 000077104 245__ $$aEffective Hausdorff Dimension in General Metric Spaces 000077104 260__ $$c2018 000077104 5060_ $$aAccess copy available to the general public$$fUnrestricted 000077104 5203_ $$aWe 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. 000077104 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/PSI2014-62092-EXP$$9info:eu-repo/grantAgreement/ES/MINECO/TIN2016-80347-R 000077104 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000077104 590__ $$a0.603$$b2018 000077104 591__ $$aMATHEMATICS$$b208 / 313 = 0.665$$c2018$$dQ3$$eT3 000077104 591__ $$aCOMPUTER SCIENCE, THEORY & METHODS$$b94 / 104 = 0.904$$c2018$$dQ4$$eT3 000077104 592__ $$a0.475$$b2018 000077104 593__ $$aTheoretical Computer Science$$c2018$$dQ2 000077104 593__ $$aComputational Theory and Mathematics$$c2018$$dQ2 000077104 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000077104 7102_ $$15007$$2570$$aUniversidad de Zaragoza$$bDpto. Informát.Ingenie.Sistms.$$cÁrea Lenguajes y Sistemas Inf. 000077104 773__ $$g62, 7 (2018), 1620-1636$$pTheor. Comput. Syst.$$tTHEORY OF COMPUTING SYSTEMS$$x1432-4350 000077104 8564_ $$s375984$$uhttps://zaguan.unizar.es/record/77104/files/texto_completo.pdf$$yPostprint 000077104 8564_ $$s54528$$uhttps://zaguan.unizar.es/record/77104/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000077104 909CO $$ooai:zaguan.unizar.es:77104$$particulos$$pdriver 000077104 951__ $$a2019-11-27-15:48:13 000077104 980__ $$aARTICLE