TITLE: Kolmogorov continuity theorem for Banach space valued random processes
QUESTION [5 upvotes]: I am interested in the Kolmogorov continuity theorem. I would like to know if this theorem holds for Banach space valued random processes (probably separable Banach space). I cannot find a paper or a textbook that contains a version of the Kolmogorov continuity theorem for Banach space valued random processes. My questions are as follows:

does the Kolmogorov continuity theorem hold for Banach space valued random processes;
where can I find a paper or a textbook that contains the statement and the proof of the Kolmogorov continuity theorem for Banach space valued random processes?

Any help is much appreciated!

REPLY [5 votes]: Theorem 3.23 on Kallenberg's "Foundations of Modern Probability" (the page might not be available in Google Books :( ). You just need a complete metric space and $\mathbb{R}^d$ as index space.
In my opinion Kallenberg's book is THE source for general theorems in probability :)