# Arithmetic progressions in sets of fractional dimension - Mathematics > Classical Analysis and ODEs

Abstract: Let $E\subset r$ be a closed set of Hausdorff dimension $\alpha$. We provethat if $\alpha$ is sufficiently close to 1, and if $E$ supports aprobabilistic measure obeying appropriate dimensionality and Fourier decayconditions, then $E$ contains non-trivial 3-term arithmetic progressions.

Author: Izabella Laba, Malabika Pramanik

Source: https://arxiv.org/