Об одном применении теоремы А.Н. Колмогорова

Чебышевский сборник. 2025. Т. 26. № 5. С. 203–220.

Соболев В. Н., Фролов А. А.

In the article, on the class K 0 of infinite binary sequences without the runs of ones, a
consistent probability distribution P is constructed which is induced by a time-homogeneous
Markov chain with a one-step transition matrix P𝜑 , and is completely determined by the
golden ratio 𝜑. Using a Markov chain to construct a probability measure P allows us to apply
Kolmogorov’s existence theorem. The asymptotic distribution of the subclass K 0 of infinite
binary sequences without the runs of ones starting with zero coincides with the analogous
asymptotic distribution of the classical equiprobable scheme . And in this case, the asymptotic
distribution of the class K 0 coincides with the probability P(K 0)

Keywords: entropy, Markov chains, марковские цепи, uniform disribution, равномерное распределение, Kolmogorov’s existence theore, теорема Колмогорова, энтропия