Hausdorff dimension of the probability measure with independent $Q_\infty$-symbols

Olena Smiian

Institute of Mathematics Conferences, Sixth International Conference on Analytic Number Theory and Spatial Tessellations

Olena Smiian

Building: Mykhailo Drahomanov National Pedagogical University
Room: Room C
Date: 2018-09-27 05:20 PM – 17:35
Last modified: 2018-09-24

Abstract

We study a problem for the determination Hausdorff dimension of the probability measure with independent $Q_\infty$-symbols. In "Ergodic properties of $Q_\infty$-expansion and fractal properties of probability measure with independent $Q_\infty$-symbols" the authors have proved an explicit formula for the determination of the corresponding dimension for the i.i.d-case. In this paper we give a formula for Hausdorff dimension of the probability measure with independent (not necessarily identically distributed) $Q_\infty$-symbols.