Israel Journal of Mathematics

, Volume 60, Issue 3, pp 333–344 | Cite as

Construction of sets of positive measure not containing an affine image of a given infinite structure

  • J. Bourgain


This paper deals with the problem of existence of infinite structures in euclidean space such that every set of positive measure contains an affine image of it. We contribute to P. Erdös’ question about sequences in the real line, by showing that no triple sum of infinite sets has this property.


Positive Measure Finite Subset Arithmetic Progression Image Measure Gaussian Measure 
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Copyright information

© Hebrew University 1987

Authors and Affiliations

  • J. Bourgain
    • 1
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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