We consider algebras of Bernoulli distributions, i. e. sets of distributions that are closed under transformations defined by substituting independent random variables for variables of a Boolean function from a given system. We establish that unless the transforming functions are unary the set of algebra’s limits point is either empty, one-element, or at least countable.

Bernoulli random variable, Boolean function, algebra, limit point

Mathematical problems and theory of numerical methods

Yashunsky Alexey Dmitrievich,  alexey.yashunsky@gmail.com,  orcid.org/0000-0002-3297-7444,  KIAM RAS