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Distribution of values of classic singular Cantor function of random argument. (English) Zbl 1440.11147

Summary: Let \(X\) be a random variable with independent ternary digits and let \(y=F(x)\) be a classic singular Cantor function. For the distribution of the random variable \(Y=F(X)\), the Lebesgue structure (i.e., the content of discrete, absolutely continuous and singular components), the structure of its point and the continuous spectra are exhaustively studied.

MSC:

11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
26A30 Singular functions, Cantor functions, functions with other special properties
28A80 Fractals
60G30 Continuity and singularity of induced measures
60G50 Sums of independent random variables; random walks
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