A strengthening of a theorem of Marcinkiewicz

Volume 95 / 2011

Konstantin E. Tikhomirov Banach Center Publications 95 (2011), 369-383 MSC: 42A50, 42A99. DOI: 10.4064/bc95-0-23


We consider a problem of intervals raised by I. Ya. Novikov in [Israel Math. Conf. Proc. 5 (1992), 290], which refines the well-known theorem of J. Marcinkiewicz concerning structure of closed sets [A. Zygmund, Trigonometric Series, Vol. I, Ch. IV, Theorem 2.1]. A positive solution to the problem for some specific cases is obtained. As a result, we strengthen the theorem of Marcinkiewicz for generalized Cantor sets.


  • Konstantin E. TikhomirovDepartment of Mechanics and Mathematics
    Samara State University
    Ak. Pavlov, 1
    443011, Samara, Russia

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