Свойство выпуклости взаимных мультифрактальных размерностей

N. Yu. Svetova

Petrozavodsk State University, Faculty of Mathematics

Abstract: It has received that the mutual packing dimension of subset $E$ of set $\mathrm{supp}~\mu\cap\mathrm{supp}~\nu$ for Borel probability measures $\mu$ and $\nu$ is convex, but the mutual Hausdorff dimension of $E$ satisfies the condition of weak convexity.

UDC: 511, 514.8, 530.1