Sets with doubleton sections, good sets and ergodic theory

Tom 173 / 2002

A. Kłopotowski, M. G. Nadkarni, H. Sarbadhikari, S. M. Srivastava Fundamenta Mathematicae 173 (2002), 133-158 MSC: Primary 60A05, 47A35; Secondary 28D05, 37Axx. DOI: 10.4064/fm173-2-3

Streszczenie

A Borel subset of the unit square whose vertical and horizontal sections are two-point sets admits a natural group action. We exploit this to discuss some questions about Borel subsets of the unit square on which every function is a sum of functions of the coordinates. Connection with probability measures with prescribed marginals and some function algebra questions is discussed.

Autorzy

  • A. KłopotowskiInstitut Galilée
    Université Paris XIII
    93430 Villetaneuse Cedex, France
    e-mail
  • M. G. NadkarniDepartment of Mathematics
    University of Mumbai
    Kalina, Mumbai, India 400098
    e-mail
  • H. SarbadhikariStat-Math Unit
    Indian Statistical Institute
    203 B. T. Road
    Calcutta, India 700035
    e-mail
  • S. M. SrivastavaStat-Math Unit
    Indian Statistical Institute
    203 B. T. Road
    Calcutta, India, 700035
    e-mail

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