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Let X be an abstract set and L a lattice of subsets of X. I(L) denotes the non-trivial zeroone valued finitely additive measures on A(L), the algebra generated by L, and IR(L) those elements ofI(L) that are L-regular. It is known that I(L)=IR(L) if and only if L is an algebra. We first give severalnew proofs of this fact and a number of characterizations of this in topologicial terms

On regular and sigma-smooth two valued measures and lattice generated topologies