# On the dimension of self-similar measures with complicated overlaps

## TL;DR

This paper studies the Hausdorff dimension of invariant measures generated by a specific iterated function system with overlaps, providing results that hold for almost every parameter choice using existing theoretical frameworks.

## Contribution

It extends understanding of the Hausdorff dimension for self-similar measures with overlaps by applying and combining recent theoretical results.

## Key findings

- Determines the Hausdorff dimension for almost all parameter values.
- Utilizes Feng and Hu's results along with Kamalutdinov and Tetenov's work.
- Provides a comprehensive analysis of overlaps in self-similar measures.

## Abstract

In this paper, we investigate the Hausdorff dimension of the invariant measures of the iterated function system (IFS) $\{\alpha x, \beta x, \gamma x+(1-\gamma)\}$. We provide an "almost every" type result by a direct application of the results of Feng and Hu; and Kamalutdinov and Tetenov.