000169450 001__ 169450 000169450 005__ 20260227133540.0 000169450 0247_ $$2doi$$a10.1007/978-3-031-95908-0_21 000169450 0248_ $$2sideral$$a148350 000169450 037__ $$aART-2025-148350 000169450 041__ $$aeng 000169450 100__ $$0(orcid)0000-0002-9109-5337$$aMayordomo, Elvira$$uUniversidad de Zaragoza 000169450 245__ $$aA Point to Set Principle for Finite-State Dimension 000169450 260__ $$c2025 000169450 5060_ $$aAccess copy available to the general public$$fUnrestricted 000169450 5203_ $$aEffective dimension has proven very useful in geometric measure theory through the point-to-set principle [9] that characterizes Hausdorff dimension by relativized effective dimension. Finite-state dimension is the least demanding effectivization in this context [3] that among other results can be used to characterize Borel normality [2]. In this paper we prove a characterization of finite-state dimension in terms of information content of a real number at a certain precision. We then use this characterization to give a robust concept of relativized normality and prove a finite-state dimension point-to-set principle. We finish with an open question on the equidistribution properties of relativized normality. 000169450 536__ $$9info:eu-repo/grantAgreement/ES/DGA/T64-20R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2019-104358RB-I00 000169450 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000169450 655_4 $$ainfo:eu-repo/semantics/conferenceObject$$vinfo:eu-repo/semantics/acceptedVersion 000169450 7102_ $$15007$$2570$$aUniversidad de Zaragoza$$bDpto. Informát.Ingenie.Sistms.$$cÁrea Lenguajes y Sistemas Inf. 000169450 773__ $$g15764 (2025), 299-304$$pLect. notes comput. sci.$$tLecture Notes in Computer Science$$x0302-9743 000169450 8564_ $$s272511$$uhttps://zaguan.unizar.es/record/169450/files/texto_completo.pdf$$yPostprint 000169450 8564_ $$s1019515$$uhttps://zaguan.unizar.es/record/169450/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000169450 909CO $$ooai:zaguan.unizar.es:169450$$particulos$$pdriver 000169450 951__ $$a2026-02-27-12:35:55 000169450 980__ $$aARTICLE