Kolmogorov extension theorem: Difference between revisions

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{{About|a theorem deals with stochastic processes|a theorem deals with extension of pre-measure|Hahn–Kolmogorov theorem}}

In [[mathematics]], the '''Kolmogorov extension theorem''' (also known as '''Kolmogorov existence theorem''' or '''Kolmogorov consistency theorem''') is a [[theorem]] that guarantees that a suitably "consistent" collection of [[finite-dimensional distribution]]s will define a [[stochastic process]]. It is credited to the [[Soviet UnionRussia|SovietRussian]] [[mathematician]] [[Andrey Kolmogorov|Andrey Nikolaevich Kolmogorov]].<ref>{{cite book | author=Øksendal, Bernt | title=Stochastic Differential Equations: An Introduction with Applications | publisher=Springer |___location=Berlin | year=2003 |edition=Sixth | isbn=3-540-04758-1 |page=11 |url=https://books.google.com/books?id=VgQDWyihxKYC&pg=PA11 }}</ref>

==Statement of the theorem==