Author:
Pratsiovytyi M.,Ratushniak S.,Symonenko Yu.,Shpytuk D.
Abstract
We consider distribution of random variable $\xi=\tau+\eta$, where $\tau$ and $\eta$ independent random variables, moreover $\tau$ has classic Cantor type distribution and $\eta$ is a random variable with independent identically distributed digits of the nine-digit representation. With additional conditions for the distributions of the digits $\eta$, sufficient conditions for the singularity of the Cantor type of the distribution $\xi$ are specified. To substantiate the statements, a topological-metric analysis of the representation of numbers $x\in [0;2]$ in the numerical system with base $9$ and a seventeen-symbol alphabet (a set of numbers) is carried out. The geometry (positional and metric) of this representation is described by the properties of the corresponding cylindrical sets.
Publisher
Yuriy Fedkovych Chernivtsi National University
Subject
Computer Science Applications,History,Education
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