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)) by π ν(B)= ∫ M(R d) η(B) dν(η), for B⊂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.