A combinatorial proof of Marstrand's theorem for products of regular Cantor sets

被引：4

作者：

Lima, Yuri ^{[1
]}

Moreira, Carlos Gustavo ^{[1
]}

机构：

[1] Inst Nacl Matemat Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil

来源：

EXPOSITIONES MATHEMATICAE | 2011年 / 29卷 / 02期

关键词：

Cantor sets; Hausdorff dimension; Marstrand theorem; HAUSDORFF DIMENSION; PROJECTIONS;

D O I：

10.1016/j.exmath.2011.01.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a paper from 1954 Marstrand proved that if K subset of R(2) has a Hausdorff dimension greater than 1, then its one-dimensional projection has a positive Lebesgue measure for almost all directions. In this article, we give a combinatorial proof of this theorem when K is the product of regular Cantor sets of class C(1+alpha), alpha > 0, for which the sum of their Hausdorff dimension is greater than 1. (C) 2011 Elsevier GmbH. All rights reserved.

引用

页码：231 / 239

页数：9

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