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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-23,
author = {Konstantin E. Tikhomirov},
title = {A strengthening of a theorem of Marcinkiewicz},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {369-383},
zbl = {1243.42020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-23}
}
Konstantin E. Tikhomirov. A strengthening of a theorem of Marcinkiewicz. Banach Center Publications, Tome 95 (2011) pp. 369-383. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-23/