Topological Aspects of the Product of Lattices

Let X be an arbitrary nonempty set and L a lattice of subsets of X such that ∅, X∈L. A(L) denotes the algebra generated by L, and M(L) denotes those nonnegative, finite, finitely additive measures on A(L). In addition, I(L) denotes the subset of M(L) which consists of the nontrivial zero-one valued measures. The paper gives detailed analysis of products of lattices, their associated Wallman spaces, and products of a variety of measures.