A strengthening of a theorem of Marcinkiewicz
Volume 95 / 2011
Banach Center Publications 95 (2011), 369-383
MSC: 42A50, 42A99.
DOI: 10.4064/bc95-0-23
Abstract
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.
