Abstract

By an Alexandrov lattice we mean a δ normal lattice of subsets of an abstract set X, such that the set of -regular countably additive bounded measures is sequentially closed in the set of -regular finitely additive bounded measures on the algebra generated by with the weak topology.For a pair of lattices 12 in X sufficient conditions are indicated to determine when 1 Alexandrov implies that 2 is also Alexandrov and vice versa. The extension of this situation is given where T:XY and 1 and 2 are lattices of subsets of X and Y respectively and T is 12 continuous.