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Topological and metric properties of distributions of random variables represented by the alternating Lüroth series with independent elements. (English) Zbl 1362.60005

Summary: In the paper we consider the distributions of random variables represented by the alternating Lüroth series (\(\widetilde L\)-expansion). We study Lebesgue structure, topological, metric and fractal properties of these random variables.We prove that random variable with independent \(\widetilde L\)-symbols has a pure discrete, pure absolutely continuous or pure singularly continuous distribution. We describe topological and metric properties of the spectra of distributions of random variables as well as properties of their probability distribution functions.

MSC:

60B99 Probability theory on algebraic and topological structures
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
26A30 Singular functions, Cantor functions, functions with other special properties
28A80 Fractals
60E10 Characteristic functions; other transforms
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