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New page: '''Ergodic Theory''' is a mathematical theory of random processes in discrete or continuous time. Such a process is called ergodic if all averages over time are the same with probability o...
'''Ergodic Theory''' is a mathematical theory of random processes in discrete or continuous time. Such a process is called ergodic if all averages over time are the same with probability one, and equal to the expectation value of the quantity considered. A more mathematical definition is: the probability distribution of the process is extremal among the shift invariant ones. The term was coined by [[Ludwig Boltzmann]] in the 19-th century to designate a hypothesis which he made about statistical mechanical systems in order to justify the use of equilibrium probability densities. The first ergodic theorems were proved by [[John von Neumann]] and [[George David Birkhoff]].
[[category:mathematics]]
[[category:mathematics]]