A note on Hausdorff measures of self-similar sets in R^d

We prove that for all \(s\in(0,d)\) and \(c\in (0,1)\) there exists a self-similar set \(E\subset\mathbf{R}^d\) with Hausdorff dimension \(s\) such that \(\mathcal{H}^s(E)=c|E|^s\). This answers a question raised by Zhiying Wen [16]