Abstract:
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 ξ= ∑∞ j=1 ξjr-j is normal with respect to the radix β. The proof is based on the Gelfand-Baker estimate for the absolute value of a linear form in the logarithms of algebraic numbers.