Sixty years of fractal projections

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Abstract

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand’s projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.
Original languageEnglish
Title of host publicationFractal Geometry and Stochastics V
EditorsCristoph Bandt, Kenneth J. Falconer, Martina Zähle
Place of PublicationBasel
PublisherBirkhauser
Pages3-25
Number of pages23
ISBN (Electronic)9783319186603
ISBN (Print)9783319186597
DOIs
Publication statusPublished - 31 Jul 2015
EventFractal Geometry and Stochastics V - Tabarz, Germany
Duration: 24 Mar 201429 Mar 2014

Publication series

NameProgress in Probability
Volume70
ISSN (Print)1050-6977

Conference

ConferenceFractal Geometry and Stochastics V
Country/TerritoryGermany
CityTabarz
Period24/03/1429/03/14

Keywords

  • Fractals
  • Projections
  • Dimensions
  • Measure

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