Problems in strong uniform distribution

Rok, strany: 2014, 51 - 64

In 1923 A. Khinchin asked if given any $B \subseteq [0,1)$ of positive Lebesgue measure, we have $((1) / (N)) \# \{n: 1≤ n ≤ N: \{nx \} \in B \} \to |B|$ 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 authors survey contributions to this subject since then.

ISO 690:

Chan, K., Nair, R. 2014. Problems in strong uniform distribution. In Tatra Mountains Mathematical Publications, vol. 59, no.2, pp. 51-64. 1210-3195.

APA:

Chan, K., Nair, R. (2014). Problems in strong uniform distribution. Tatra Mountains Mathematical Publications, 59(2), 51-64. 1210-3195.