Maximizing dimension for Bernoulli measures and the Gauss map

TL;DR

This paper proves the existence of a countable state Bernoulli measure that maximizes the dimension of its image under the continued fraction expansion, providing a concise proof of this property.

Contribution

It offers a short proof demonstrating the existence of a Bernoulli measure with maximal dimension under continued fraction transformation.

Findings

Existence of a measure maximizing dimension established

Short proof provided for the maximization property

Focus on Bernoulli measures and continued fractions

Abstract

We give a short proof that there exists a countable state Bernoulli measure maximizing the dimension of their images under the continued fraction expansion.