Let ξ1,ξ2,. . . be a random sequence of r-ary digits, r ∈ N\{1}, connected into an ergodic Markov chain. Let β > 1 be an algebraic number such that the ratio log β/log r is irrational. Then with probability one, the number ...

It is shown that, under the action of random digitwise decaying perturbations not changing the spectrum of the limit frequencies of r-adic digits, an arbitrary real number written in the r-adic number systembecomes almost ...

Let r, g ≥ 2 be integers such that log g/log r is irrational. We show that under r-digitwise random perturbations of an expanded to base r real number x, which are small enough to preserve r-digit asymptotic frequency ...