A Bernoulli scheme is the measure-preserving shift on a product probability space whose coordinates are independent and have a common statistical distribution. It is the dynamical-system analog of independent Bernoulli trials. For a countable discrete one-coordinate statistical distribution, its Kolmogorov entropy is the Shannon entropy of that statistical distribution, possibly infinite.
Bernoulli Scheme
See also
Bernoulli Action, Bernoulli Trial, Ergodic TheoryExplore with Wolfram|Alpha
References
Walters, P. An Introduction to Ergodic Theory. New York: Springer-Verlag, 1982.Cite this as:
Weisstein, Eric W. "Bernoulli Scheme." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BernoulliScheme.html