Hausdorff Dimension and Non-degenerate Families of Projections

被引：12

作者：

Jarvenpaa, Esa ^{[1
]}

Jarvenpaa, Maarit ^{[1
]}

Keleti, Tamas ^{[2
]}

机构：

[1] Univ Oulu, Dept Math Sci, Oulu 90014, Finland

[2] Eotvos Lorand Univ, Dept Anal, H-1117 Budapest, Hungary

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2014年 / 24卷 / 04期

基金：

芬兰科学院;

关键词：

Projection; Hausdorff dimension; Measure;

D O I：

10.1007/s12220-013-9407-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study parameterized families of orthogonal projections for which the dimension of the parameter space is strictly less than that of the Grassmann manifold. We answer the natural question of how much the Hausdorff dimension may decrease by verifying the best possible lower bound for the dimension of almost all projections of a finite measure. We also show that a similar result is valid for smooth families of maps from the n-dimensional Euclidean space to the m-dimensional one.

引用

页码：2020 / 2034

页数：15

共 14 条

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[Anonymous], 1995, Geometry of Sets and Measures in Euclidean Spaces

[2]

Bourgain J., 1991, GEOM FUNCT ANAL, V1, P1

[3]

Falconer K., 1997, Techniques in Fractal Geometry

[4] CONTINUITY PROPERTIES OF K-PLANE INTEGRALS AND BESICOVITCH SETS [J].