A self-similar measure with dense rotations, singular projections and discrete slices

被引：6
|
作者：
Rapaport, Ariel
机构：
来源：
ADVANCES IN MATHEMATICS | 2017年 / 321卷
关键词：
Self-similar measure; Singular measure; Dimension conservation; FRACTAL MEASURES; BERNOULLI CONVOLUTIONS; SETS; HAUSDORFF;
D O I：
10.1016/j.aim.2017.10.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct a planar homogeneous self-similar measure, with strong separation, dense rotations and dimension greater than 1, such that there exist lines for which dimension conservation does not hold and the projection of the measure is singular. In fact, the set of such directions is residual and the typical slices of the measure, perpendicular to these directions, are discrete. (c) 2017 Elsevier Inc. All rights reserved.
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页码：529 / 546
页数：18
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