# Dimension growth for iterated sumsets

25 Nov 2018 Fraser Jonathan M. Howroyd Douglas C. Yu Han

We study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set $F \subseteq \mathbb{R}$ satisfies $\overline{\dim}_\text{B} F+F > \overline{\dim}_\text{B} F$ or even $\dim_\text{H} n F \to 1$. Our results apply to, for example, all uniformly perfect sets, which include Ahlfors-David regular sets... (read more)

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