In 1923 A. Khinchin asked if given any B ? [0, 1) of positive Lebesgue measure, we have #{n : 1 ≤ n ≤ N : {nx} ε B} → |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.
Problems in strong uniform distribution
Kwo Lik Chan;
2014-01-01
Abstract
In 1923 A. Khinchin asked if given any B ? [0, 1) of positive Lebesgue measure, we have #{n : 1 ≤ n ≤ N : {nx} ε B} → |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.File in questo prodotto:
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