The Hausdorff measure of the self-similar sets. The Koch curve (Q1267230)

In this paper the author proved that, for a self-similar set \(F\) satisfying the open set condition, \(H^s(F)= H^s_\delta(F)\) for any \(\delta>0\) and \(H^s(F\cap U)\leq| U|^s\), where \(s\) is the Hausdorff dimension of \(F\) and \(U\subset\mathbb{R}^n\) is a measurable set with diameter \(| U|> 0\). Applying these results to the von Koch curve, the author gives a negative answer to Marion's conjecture [\textit{J. Marion}, Ann. Sci. Math. Qué. 11, 111-132 (1987; Zbl 0624.28003)].