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Measure density for set decompositions and uniform distribution. (English) Zbl 1388.11045

Summary: The aim of this paper is to extend the concept of measure density introduced by R. C. Buck [Am. J. Math. 68, 560–580 (1946; Zbl 0061.07503)] for finite unions of arithmetic progressions, to arbitrary subsets of \(\mathbb{N}\) defined by a given system of decompositions. This leads to a variety of new examples and to applications to uniform distribution theory.

MSC:

11K06 General theory of distribution modulo \(1\)
11J71 Distribution modulo one
11A67 Other number representations
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures

Citations:

Zbl 0061.07503
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Full Text: DOI arXiv

References:

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