Given a subsequence of a uniformly distributed sequence, relations between the asymptotic densities of sets of its indices and the Lebesgue measure of the set of all its limit points are studied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-3,
author = {Ladislav Mi\v s\'\i k},
title = {On limit points of subsequences of uniformly distributed sequences},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {333-338},
zbl = {1307.11084},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-3}
}
Ladislav Mišík. On limit points of subsequences of uniformly distributed sequences. Acta Arithmetica, Tome 166 (2014) pp. 333-338. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-3/