ON ALEXANDROV LATTICES

By an Alexandrov lattice we mean a δ normal lattice of subsets of an abstract set X, such that the set of ℒ-regular countably additive bounded measures is sequentially closed in the set of ℒ-regular finitely additive bounded measures on the algebra generated by ℒ with the weak topology. For a pair of lattices ℒ_1 ⊂ ℒ_2 in X sufficient conditions are indicated to determine when ℒ_1 Alexandrov implies that ℒ_2is also Alexandrov and vice versa. The extension of this situation is given where T: X→Y and ℒ_1 and ℒ_2 are lattices of subsets of X and Y respectively and T is ℒ_1−ℒ_2 continuous.