# A von Neumann theorem for uniformly distributed sequences of partitions

@article{Carbone2009AVN, title={A von Neumann theorem for uniformly distributed sequences of partitions}, author={Ingrid Carbone and Aljo{\vs}a Vol{\vc}i{\vc}}, journal={Rendiconti del Circolo Matematico di Palermo}, year={2009}, volume={60}, pages={83-88} }

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann’s theorem on permutations of dense sequences and uniformly distributed sequences of points.

## 12 Citations

### A random von Neumann theorem for uniformly distributed sequences of partitions

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Abstract In this paper, we prove a theorem that confirms, under a supplementary condition, a conjecture concerning random permutations of sequences of partitions of the unit interval.

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In this paper, we will study uniformly distributed sequences of partitions of [0, 1], a concept which has been introduced by Kakutani (Measure Theory 541:369–375, 1976). We will construct new…

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In this paper, we will study uniformly distributed sequences of partitions of (0,1), a concept which has been introduced by Kakutani (Measure Theory 541:369-375, 1976). We will construct new families…

### Discrepancy of LS-sequences of partitions and points

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In this paper, we study a countable family of uniformly distributed sequences of partitions, called LS-sequences of partitions, and we give a precise estimate of their discrepancy. Among these…

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The interest for uniformly distributed (u.d.) sequences of points, in particular for sequences with small discrepancy, arises from various applications. For instance, low-discrepancy sequences, which…

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Another algorithm is presented which coincides with the classical one for van der Corput sequences and is simpler to compute than the original construction, and a nice geometrical explanation of this "magical" operation is given.

### A van der Corput-type algorithm for LS-sequences of points

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In this paper we associate to any $LS$-sequence of partitions ${\rho_{L,S}^n}$ the corresponding $LS$-sequence of points ${\xi_{L,S}^n}$ obtained reordering the points of each partition with an…

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In this paper, we will study uniformly distributed sequences of partitions of [0, 1], a concept which has been introduced by Kakutani (Measure Theory 541:369–375, 1976). We will construct new…

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