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May 9, 2019 at 22:05 vote accept Aryeh Kontorovich
May 9, 2019 at 8:10 comment added Hollis Williams I'm fairly sure Einstein was only interested in Brownian motion as a physical problem and did not particularly care about measures on Banach spaces.
May 8, 2019 at 2:16 comment added user44143 Einstein's comments are translated here: einsteinpapers.press.princeton.edu/vol2-trans/144
May 8, 2019 at 0:28 comment added Christian Remling This isn't very relevant to the example as an answer to the actual question, but I think it's safe to assume that Einstein was blissfully unaware of all these mathematical issues, and probably the thought that someone might want to prove existence of BM would have seemed mildly absurd to him (just as an attempt to prove the existence of the keyboard I'm using to type this comment might seem to me).
May 7, 2019 at 20:28 history answered Nate Eldredge CC BY-SA 4.0