O(X,Y) the following conditions are O(X, Y), i.e., G is ergodic;

doi:10.1201/9780203913574-53

ABSTRACT

G = G1 + (1 - )G2 Pse(X × Y) = ex Ps(X × Y). Since this is a proper convex combination of measures in Ps(X×Y), we have G1 = G2 = G for Pse(X). Hence G1 = G2 = G (mod Pse(X)). Therefore, (2) holds.