Convergence of Brownian motions on RCD*(K,N) spaces
Abstract
Suppose that a sequence of metric measure spaces Xn=(Xn, dn, mn) satisfies RCD*(K,N) with Diam(Xn) <D and mn(Xn)=1. Then Sturm's D-convergence of Xn is equivalent to the weak convergence of the laws of Brownian motions on Xn.
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