PACKING MEASURE AND DIMENSION OF LOOSELY SELF-SIMILAR SETS

  • TAE HEE KIM (Department of Mathematics Kyungpook National University) ;
  • MI RYEONG LEE (Department of Mathematics Kyungpook National Universit) ;
  • SANG HUN LEE (Department of Mathematics Kyungpook National Universit) ;
  • HUNG HWAN LEE (Department of Mathematics Kyungpook National University)
  • Published : 1998.10.01

Abstract

Let K be a loosely self-similar set. Then a-dimensional packing measure of K is the same as that of a Borel subset K( $r_1^{\alpha}$ㆍㆍㆍ$r_{m}$ $^{\alpha}$/) of K. And packing dimension of K is equal to that of K\K( $r_1^{\alpha}$ㆍㆍㆍ $r_{m}$ $^{\alpha}$/) and K( $r_1^{\alpha}$ㆍㆍㆍ $r_{m}$ $^{\alpha}$/).X> $^{\alpha}$/)).