Positive-measure intersections of Bedford-McMullen carpets under similitudes

Ding-Kun Hu, Huo-Jun Ruan, Jian-Ci Xiao

Let $K=K(n,m,\Gamma )$ be a Bedford-McMullen carpet with $n>m\ge 2$ and $1<\#\Gamma <nm$, and let $\mu$ be a self-affine measure on $K$ with strictly positive weights. We prove that every simili…