Packing dimension and Cartesian products

被引：10

作者：

Bishop, CJ ^{[1
]}

Peres, Y ^{[1
]}

机构：

[1] UNIV CALIF BERKELEY,DEPT STAT,BERKELEY,CA 94720

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1996年 / 348卷 / 11期

关键词：

Hausdorff dimension; packing dimension; Cartesian product; tree;

D O I：

10.1090/S0002-9947-96-01750-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for any analytic set A in R(d), its packing dimension dim, (A) can be represented as sup(B){dim(H)(A x B) - dim(H)(B)}, where the supremum is over all compact sets B in R(d), and dim, denotes Hausdorff dimension. (The lower bound on packing dimension was proved by Tricot in 1982.) Moreover, the supremum above is attained, at least if dim(P) (A) < d. In contrast, we show that the dual quantity inf(B){dim(P)(A x B) - dim(P) (B)}, is at least the ''lower packing dimension'' of A, but can be strictly greater. (The lower packing dimension is greater than or equal to the Hausdorff dimension.)

引用

页码：4433 / 4445

页数：13