Journal d'Analyse Mathématique

, Volume 112, Issue 1, pp 193–236 | Cite as

The discretized sum-product and projection theorems

  • Jean Bourgain


We give a new presentation of the discrete ring theorem for sets of real numbers [B]. Special attention is given to the relation between the various parameters. As an application, new Marstrand type projection theorems are obtained and formulated either in terms of box or Hausdorff dimension. It is shown that the dimension of the projections satisfies a nontrivial lower bound outside a very sparse set of exceptional directions.


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Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  1. 1.Institute for Advanced StudySchool of MathematicsPrincetonUSA

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