Boolean algebras of lattice uniformities and decompositions of modular functions (Q1042611)

The author studies decomposition theorems for modular functions on lattices which generalize decomposition theorems for measures on Boolean algebras, and the related question when a system of lattice uniformities is a Boolean algebra. He proves that a decomposition theorem of a certain type holds true if and only if a system of lattice uniformities is a Boolean algebra of pairwise permutable uniformities. This result leads to a detailed discussion of the latter condition.