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Any sequence $x = {(x_{k})}_{k = 1}^{\infty}$ of distinct numbers from [0,1] generates a binary tree by storing the numbers consecutively at the nodes according to a left-right algorithm (or equivalently by sorting the numbers according to the Quicksort algorithm). Let $H_{n} (x)$ be the height of the tree generated by $x_{1}, \dots, x_{n} .$ Obviously $\frac{log n}{log 2} - 1 \leq H_{n} (x) \leq n - 1 .$ If the sequences $x$ are generated by independent random variables having the uniform distribution on [0, 1], then it is well known that there exists $c$ > $0$ such that $H_{n} (x) \sim c log n$ as $n \to \infty$ for almost all sequences $x$ . Recently...

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Über die asymptotische Verteilung reeller Zahlen mod l

Über die Diskrepanz gewisser Folgen Mod 1 mit Hilfe Diophantischer Approximation.

Über die Gleichverteilung von Zahlen mod. Eins

Über ein Problem in der Theorie der C-Gleichverteilung.

Über eine Klasse von gleichverteilten Folgen

Über einige Beispiele für Anwendungen der Theorie der Gleichverteilung

Un ensemble exceptionnel pour un problème de répartition modulo 1.

Un problème d'équirépartition modulo 1 lié aux partitions

Un théorème de finitude

Une modification multiplicative des nombres $g$ normaux

Une remarque sur les suites équiréparties à croissance lente

Uniform Dilations.

Uniform Distribution and Diophantine Inequalities.

Uniform Distribution and the Mean Ergodic Theorem.

Uniform distribution in locally compact groups.

Uniform distribution modulo one and binary search trees

Uniform distribution of generalized polynomials of the product type

Uniform distribution preserving mappings

Uniform distrubution, positive trigonometric polynomials and difference sets

Uniformly distributed sequences mod 1 and Cantor's series representation

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