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==A more general form of the theorem==
The Kolmogorov extention theorem gives us conditions for a collection of measures on Euclidean spaces to be the finite-dimensional distributions of some <math>\mathbb{R}^{n}</math>-valued stochastic process, but the assumption that the state space be <math>\mathbb{R}^{n}</math> is unnecessary. In fact, any collection of measurable spaces together with a collection of [[inner regular
Let <math>T</math> be any set, and let <math> \{ (\Omega_t, \mathcal{F}_t) \}_{t \in T} </math> be some collection of measurable spaces, and for each <math> t \in T </math>, let <math> \tau_t</math> be a Hausdorff topology on <math> \Omega_t</math>. For each subset <math>J \subset T</math>, let
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