doi:10.1007/978-3-031-95908-0_21engMayordomo, ElviraA Point to Set Principle for Finite-State DimensionART-2025-148350Effective 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.2025http://zaguan.unizar.es/record/16945010.1007/978-3-031-95908-0_21http://zaguan.unizar.es/record/169450oai:zaguan.unizar.es:169450info:eu-repo/grantAgreement/ES/DGA/T64-20Rinfo:eu-repo/grantAgreement/ES/MICINN/PID2019-104358RB-I00Lecture Notes in Computer Science 15764 (2025), 299-304All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess