- 期刊
LATTlCE SEPARATION, COSEPARATION AND REGULAR MEASURES
摘要
Let X be an arbitrary non-empty set, and let L, L_1, L_2 be lattices of subsets of X containing Ø and X. A(L)designates the algebra generated by L and M(L), these finite, non-trivial, non-negative finitely additive measures on A(L). I(L) denotes those elements of M(L) which assume only the values zero and one. In terms of a μ ∈ M(L) or I(L), various outer measures are introduced. Their properties are investigated. The interplay of measurability, smoothness of μ, regularity of μ and lattice topological properties on these outer measures is also investigated. Finally, applications of these outer measures to separation type properties between pairs of lattices L_1, L_2 whereL_1⊂L_2 are developed. In terms of measures from I(L), necessary and sufficient conditions are established forL_1 to semi-separate L_2, for L_1 to separate L_2, and finally for L_1 to coseparate L_2.
延伸閱讀
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