Kolmogorov extension theorem
Consistent set of finite-dimensional distributions will define a stochastic process / From Wikipedia, the free encyclopedia
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This article is about a theorem on stochastic processes. For a theorem on extension of pre-measure, see Hahn–Kolmogorov theorem.
In mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees that a suitably "consistent" collection of finite-dimensional distributions will define a stochastic process. It is credited to the English mathematician Percy John Daniell and the Russian mathematician Andrey Nikolaevich Kolmogorov.[1]