I'm giving a presentation in my graduate class on Kakutani's dichotomy, as presented in Durrett's Probability: Theory and Examples. To my understanding, it gives necessary and sufficient conditions on when two infinite product measures are "equivalent" or mutually singular. However, why is this an important question to figure out? The Wikipedia article I linked to above alludes to an application to Gaussian measures, but I have no experience with infinite-dimensional Gaussian measures, and don't know why one might translate one such measure. Could someone explain some application to me that doesn't require a lot of probability prerequisites?
2026-03-27 01:46:31.1774575991
Applications of Kakutani's dichotomy
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