I'm learning about infinite dimensional probability, and most resources I've consulted so far motivate things by saying there is no infinite dimensional Lebesgue/translation invariant measure that gives nontrivial measures for unit balls in a Banach space. The proposed alternative is almost always to look Gaussian measures instead. Why are they seen as the standard alternative to Lebesgue measure when doing probability in infinite dimensions?
2026-02-23 12:07:13.1771848433
Why are Gaussian measures seen as the standard measure for infinite dimensional spaces?
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