Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Bernoulli scheme is a generalization of the Bernoulli process to more than two possible outcomes. That is, it is a discrete-time stochastic process where each independent random variable may take on one of N distinct possible values, with the outcome i occurring with probability pi, with i=1,...,N. The Bernoulli scheme is a stationary stochastic process; further, it is a discrete-time Levy process. The isomorphism theorem for Bernoulli schemes, sometimes called the Ornstein isomorphism theorem, proven by Donald Ornstein in 1968, states that two Bernoulli schemes with the same entropy are isomorphic. By isomorphic, it is meant that if X and Y are two sample spaces, then there exists a function between these two that is measurable and invertible, that commutes with the measures, and that commutes with the shift operators for almost all sequences in X and Y. A simplified proof of the isomorphism theorem was given by Michael S. Keane and M. Smorodinsky in 1979.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.