Let M(R d ) denote the space of locally finite measures on R d and let M 1 (M(R d )) denote the space of probability measures on M(R d ). Define the mean measure π ν of ν M 1 (M(R d )) byπ ν (B)=∫M(R d )η(B)dν(η),forB R d .For such a measure ν with locally finite mean measure π ν , let f be a nonnegative, locally bounded test function satisfying <f,π ν >=~. ν is said to satisfy the strong law of large numbers with respect to f if <f n ,η>/<f n ,π ν > converges almost surely to 1 with respect to ν as n->~, for any increasing sequence {f n } of compactly supported functions which converges to f. ν is said to be mixing with respect to two sequences of sets {A n } and {B n } if∫M(R d )f(η(A n ))g(η(B n ))dν(η)-∫M(R d )f(η(A n ))dν(η)∫M(R d )g(η( B n ))dν(η)converges to 0 as n->~ for every pair of functions f,g C b 1 ([0,~)). It is known that certain classes of measure-valued diffusion processes possess a family of invariant distributions. These distributions belong to M 1 (M(R d )) and have locally finite mean measures. We prove the strong law of large numbers and mixing for many such distributions.