Calculation of Improper Integrals by Using Uniformly Distributed Sequences

Gogi Pantsulaia ()
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Gogi Pantsulaia: Georgian Technical University, Department of Mathematics

Chapter Chapter 1 in Applications of Measure Theory to Statistics, 2016, pp 1-18 from Springer

Abstract: Abstract A certain modified version of Kolmogorov’s strong law of large numbersStrong law of large numbers is used for an extension of the result of C. Baxa and J. Schoi $$\beta $$ engeier (2002) to a maximal set of uniformly distributed sequences in (0, 1) that strictly contains the set of all sequences having the form $$(\{\alpha n\})_{n \in \mathbf{N}}$$ for some irrational number $$\alpha $$ and having the full $$\ell _1^{\infty }$$ -measure, where $$\ell _1^{\infty }$$ denotes the infinite power of the linear Lebesgue measure $$\ell _1$$ in (0, 1).

Keywords: Uniformly Distributed Sequences; Infinite Power; Glivenko-Cantelli Theorem; Auxiliary Notions; Main Corollary (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-45578-5_1

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DOI: 10.1007/978-3-319-45578-5_1

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