On the Assouad dimension of projections

Let $F\subset {\mathbb{R}}^2$, and let ${\dim }_{\mathrm{A}}$ stand for Assouad dimension. I prove that $\dim_{$\mathrm{A}$} \pi_{e}(F) \geq \min{\dim_{$\mathrm{A}$} F,1}$forall$e \in S^{1}$ outside of a set of Hausdorff dimension zero. This is a strong variant of Marstrand’s projection theorem for Assouad dimension, whose analogue is not true for other common notions of fractal dimension, such as Hausdorff or packing dimension.