On outer measures and semi-separation of lattices

This present paper is concerned with set functions related to { 0 , 1 } two valued measures. These set functions are either outer measures or have many of the same characteristics. We investigate their properties and look at relations among them. We note in particular their association with the semi-separation of lattices. To be more specific, we define three set functions μ ″ , μ ′ , and μ ˜ related to μ ϵ I ( L ) the { 0 , 1 } two valued set functions defined on the algebra generated by the lattice of sets L st μ is a finitely additive monotone set function for which μ ( ϕ ) = 0 . We note relations among them and properties they possess.ln particular necessary and sufficient conditions are given for the semi-separation of lattices in terms of equality of set functions over a lattice of subsets. Finally the notion of I -lattice is defined, we look at some properties of these with certain other side conditions assume, and end with an application involving semi-separation and I -lattices.