Problems in strong unifrom distribution
Chan, Kwo ; Nair, Radhakrishnan
Tatra Mountains Mathematical Publications, Tome 58 (2014), / Harvested from Mathematical Institute
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In 1923 A. Khinchin asked if given any $B\subseteq [0; 1)$ of positive Lebesguemeasure, we have $ \frac{1}{N}#\{n :1 \le  n \le N : \{nx\} \in  B\}  \to | B | $for almost all $x$ with respect to Lebesgue measure. Here \{y\} denotes the fractional part of the real number $ y $ and $| A |$ denotes the Lebesgue measure of the set $ A $ in $ [0; 1) $. In 1970 J. Marstrand showed the answer is no. In this paper the author surveys contributions to this subject since then.

Publié le : 2014-01-01
DOI : https://doi.org/10.2478/tatra.v59i0.313 
@article{313,
     title = {Problems in strong unifrom distribution},
     journal = {Tatra Mountains Mathematical Publications},
     volume = {58},
     year = {2014},
     doi = {10.2478/tatra.v59i0.313},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/313}
}

Chan, Kwo; Nair, Radhakrishnan. Problems in strong unifrom distribution. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v59i0.313. http://gdmltest.u-ga.fr/item/313/