Uniform distribution of sequences
The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916 and ultimately provided common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of methods as well as their underlying principles. 1974 edition.
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The Weyl criterion
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arbitrary Borel measure Borel sets Chapter Cigler compact abelian group compact Hausdorff space compact monothetic group constant continuity set continuous function convergence Corollary Corput countable base defined Definition denote discrepancy discrete topology distributed sequences elements Erdos ergodic Example Exercise exists finite sequence given group G Haar measure Hausdorff space Hlawka holds implies individual ergodic theorem inequality integer h interval irrational Koksma Kuipers lattice points Lebesgue measure Lemma Let G Let xn locally compact abelian locally compact group Math matrix method monogenic Niederreiter nonnegative polynomial positive integer proof of Theorem Prove quotient group rational real numbers result satisfies Section sequence xn sequences in G subgroup of G subset summation method Suppose Theorem 1.1 topological group topologically isomorphic u.d. in G u.d. mod u.d. sequence uniform distribution uniformly unitary representation Weyl criterion x e G