A Point to Set Principle for Finite-State Dimension

Mayordomo, Elvira (Universidad de Zaragoza)

Resumen: Effective 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.

Idioma: Inglés

DOI: 10.1007/978-3-031-95908-0_21

Año: 2025

Publicado en: Lecture Notes in Computer Science 15764 (2025), 299-304
ISSN: 0302-9743

Financiación: info:eu-repo/grantAgreement/ES/DGA/T64-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2019-104358RB-I00

Tipo y forma: Congress (PostPrint)

Área (Departamento): Área Lenguajes y Sistemas Inf. (Dpto. Informát.Ingenie.Sistms.)