 Kolmogorov extension 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..

Let formula_1 denote some interval (thought of as "time"), and let formula_2.