On compactness of lattices

Abstract

Let X be an arbitrary set and L a lattice of subsets of X. We denote by I(L) the set of those zero-one-valued nontrivial, finitely additive measures on A(L), the algebra generated by L, and we introduce other subsets of I(L). We study compactness/normality properties either relating to a single lattice L or relating to a pair of lattices L1⊂L2 of subsets of X.