OUTER MEASURE ANALYSIS OF TOPOLOGICAL LATTICE PROPERTIES

SETIAWATI WIBISONO

《International Journal of Mathematics and Mathematical Sciences》 1997卷 (1997/12) Pp. 279-291

https://doi.org/10.1155/S0161171297000380

摘要

Let X be a set and L a lattice of subsets of X such that ∅, X ∈ L. A(L) is the algebra generated by L, M(L) the set of nontrivial, finite, normegative, finitely additive measures on A(L) and I(L) those elements of M(L) which just assume the values zero and one. Various subsets of M(L) and I(L) are included which display smoothness and regularity properties. We consider several outer measures associated with dements of M(L) and relate their behavior to smoothness and regularity conditions as well as to various lattice topological properties. In addition, their measurable sets are fully investigated. In the case of two lattices L_1, L_2, with L_1 ⊂ L_2, we present consequences of separation properties between the pair of lattices in terms of these outer measures, and further demonstrate the extension of smoothness conditions on L_1 to L_2.

關鍵字

Lattice ； measure ； associated outer measure ； regular outer measure ； weakly regular ； vaguely regular ； almost countably compact ； complement generated ； countably paracompact ； delta ； normal ； semi-separation ； separation ； coseparation