Hausdorff dimension of real numbers with bounded digit averages

Eda Cesaratto (1) , Brigitte Vallée (2)

1 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
2 Equipe AMACC - Laboratoire GREYC - UMR6072

This paper considers numeration schemes, defined in terms of dynamical systems and studies the set of reals which obey some constraints on their digits. In this general setting, (almost) all sets have zero Lebesgue measure, even though the nature of the constraints and the numeration schemes are very different. Sets of zero measure appear in many areas of science, and Hausdorff dimension has shown to be an appropriate tool for studying their nature.

Domaines: Algorithme et structure de données [cs.DS]

Eda Cesaratto, Brigitte Vallée. Hausdorff dimension of real numbers with bounded digit averages. Acta Arithmetica, 2006, pp.115-162. ⟨hal-00204779⟩