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

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Abstract

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.

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References

  1. P. Erdös, Private communication, 1983.

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  1. Institut des Hautes Etudes Scientifiques, 35, route de Chartres, 91440, Bures-sur-Yvette, France

    J. Bourgain

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  1. J. Bourgain
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Bourgain, J. Construction of sets of positive measure not containing an affine image of a given infinite structure. Israel J. Math. 60, 333–344 (1987). https://doi.org/10.1007/BF02780397

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  • DOI: https://doi.org/10.1007/BF02780397

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