Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/yet-another-proof-of-marstrand-s-theorem-93aHOCXGQ4
References (29)
-
Y. Peres, Pablo Shmerkin (2007)
Resonance between Cantor setsErgodic Theory and Dynamical Systems, 29
-
A. Besicovitch (1952)
On existence of subsets of finite measure of sets of infinite measure, 55
-
M. Rams (2002)
Packing dimension estimation for exceptional parametersIsrael Journal of Mathematics, 130
-
Carloa Moreira, J. Yoccoz (2001)
Stable intersections of regular Cantor sets with large Hausdorff dimensionsAnnals of Mathematics, 154
-
P. Mattila, Pirjo Saaranen (2008)
AHLFORS-DAVID REGULAR SETS AND BILIPSCHITZ MAPSarXiv: Metric Geometry
-
C. Moreira, J. Yoccoz (2010)
Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractaleAnnales Scientifiques De L Ecole Normale Superieure, 43
-
(1993)
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge studies in advanced mathematics -
Hall, Marshall (1947)
On the Sum and Product of Continued FractionsAnnals of Mathematics, 48
-
J. Palis, F. Takens (1993)
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors -
(2009)
Shmerkin, Resonance between Cantor sets -
M. Rams (1998)
Exceptional Parameters for Iterated Function Systems with OverlapsPeriodica Mathematica Hungarica, 37
-
A dimension formula for images of cartesian products of regular Cantor sets by differentiable real maps -
Yuri Lima, C. Moreira (2009)
A combinatorial proof of Marstrands theorem for products of regular Cantor setsInternational Journal of Biological Macromolecules
-
(2001)
A dimension formula for images of cartesian products of regular Cantor sets by differentiable real maps , in preparation Stable Intersections of Cantor Sets with Large Hausdorff Dimension -
The Markov and Lagrange spectra, Mathematical Surveys and Monographs 30 -
R. Kaufman (1968)
On Hausdorff dimension of projectionsMathematika, 15
-
R. Davies (1952)
Subsets of finite measure in analytic sets, 55
-
J. Palis, F. Takens (1993)
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations -
(1986)
The geometry of fractal sets, Cambridge Tracts in Mathematics -
J. Palis, J. Yoccoz (1997)
On the arithmetic sum of regular Cantor setsAnnales De L Institut Henri Poincare-analyse Non Lineaire, 14
-
J. Marstrand (1954)
The dimension of Cartesian product setsMathematical Proceedings of the Cambridge Philosophical Society, 50
-
(2001)
Yoccoz, Stable Intersections of Cantor Sets with Large Hausdorff Dimension -
(1968)
On Hausdorff dimension of projections, Mathematika -
M. Hochman, Pablo Shmerkin (2009)
Local entropy averages and projections of fractal measuresAnnals of Mathematics, 175
-
(2001)
Stable Intersections of Cantor Sets with Large Hausdorff Dimension -
J. Marstrand (1954)
Some Fundamental Geometrical Properties of Plane Sets of Fractional DimensionsProceedings of The London Mathematical Society
-
(1993)
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge studies in advanced -
P. Mattila (2004)
Hausdorff dimension, projections, and the Fourier transformPublicacions Matematiques, 48
-
K. Falconer (1986)
The geometry of fractal sets
- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-011-0018-3
- Publisher site
- See Article on Publisher Site
Abstract
In a paper from 1954 Marstrand proved that if K ⊂ ℝ2 is a Borel set with Hausdorff dimension greater than 1, then its one-dimensional projection has positive Lebesgue measure for almost-all directions. In this article, we give a combinatorial proof of this theorem, extending the techniques developed in our previous paper [9].
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Sep 15, 2011