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.
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