## Sequences, Discrepancies and ApplicationsThe main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory. |

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### Contents

Contents | 1 |

XII | 154 |

General Concepts of Uniform Distribution | 204 |

Copyright | |

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algorithm applications approximation arbitrary assume Beck Borel Borel measure Borel set coefficients compact compute congruential considered constant continuous function convergence convex Coquet Corollary defined definition denote digits dimension dimensional diophantine diophantine approximation discrepancy bound discrepancy system distributed sequences distribution function Drmota equation ergodic estimate exists exponential sums fc-dimensional finite sequence Fourier Furthermore Halton sequence Hence Hlawka implies inequality integers interval investigated irrational irregularities of distribution Kuipers Larcher lattice points Lebesgue measure Lemma linear recurring sequences lower bound Math measure Mendes France metric metric space mod P2 modulo Niederreiter number theory obtain polynomial positive integers problem proof of Theorem properties proved pseudorandom Quasi-Monte Carlo methods random number real numbers satisfying sequence of positive sequence xn sequence xn)n>i space subsets sufficiently large Suppose Tichy u.d. mod u.d. sequences uniform distribution uniformly upper bound weighted means Weyl's criterion