Can we take Donsker's Invariance Principle as the proof of the existence of Brownian motion?
At first I thought proving convergence to something nonexistent of course doesn't prove the existence of the limit. But then, upon rereading the statement and proof of Invariance Principle I noticed they include the existence of the limit, which is the Wiener measure. (And in turn the existence of Brownian motion via the coordinate map.) Am I missing something here? I'm asking this question because I don't remember ever seeing Invariance Principle under the heading of Existence. Thank you.