Packing Measure and Dimension of Loosely Self-Similar Sets

Commun. Korean Math. Soc. 1998 Vol. 13, No. 4, 781-789

Tae Hee Kim, Mi Ryeong Lee, Sang Hun Lee, Hung Hwan Lee Kyungpook National University, Kyungpook National University, Kyungpook National University, Kyungpook National University

Abstract : Let $K$ be a loosely self-similar set. Then $\alpha$-dimensional packing measure of $K$ is the same as that of a Borel subset $K(r_1^\alpha,\cdots,r_m^\alpha)$ of $K$. And packing dimension of $K$ is equal to that of $K\setminus K(r_1^\alpha,\cdots,r_m^\alpha)$ and $K(r_1^\alpha,\cdots,r_m^\alpha).$

Keywords : packing measure and dimension, loosely self-similar set