CONVOLUTION OF TWO SINGULAR DISTRIBUTIONS: CLASSIC CANTOR TYPE AND RANDOM VARIABLE WITH INDEPENDENT NINE DIGITS

We consider distribution of random variable $\xi=\tau+\eta$, where $\tau$ and $\eta$ independent variables, moreover has classic Cantor type is a with identically distributed digits the nine-digit representation. With additional conditions for distributions $\eta$, sufficient singularity $\xi$ are specified. To substantiate statements, topological-metric analysis representation numbers $x\in [0;2]$ in numerical system base $9$ seventeen-symbol alphabet (a set numbers) carried out. The geometry (positional metric) this described by properties corresponding cylindrical sets.