Hausdorff measure of p-Cantor sets.

Abstract

In this paper we analyze Cantor type sets constructed by the removal of open intervals whose lengths are the terms of the $p$-sequence, $\{k^{-p}\}_{k=1}^\infty$. We prove that these Cantor sets are $s$-sets, by providing sharp estimates of their Hausdorff measure and dimension. Sets of similar structure arise when studying the set of extremal points of the boundaries of the so-called random stable zonotopes.