Measures on coallocation and normal lattices

Jack-Kang Chan

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-18

Abstract:

Let ℒ 1 and ℒ 2 be lattices of subsets of a nonempty set X . Suppose ℒ 2 coallocates ℒ 1 and ℒ 1 is a subset of ℒ 2 . We show that any ℒ 1 -regular finitely additive measure on the algebra generated by ℒ 1 can be uniquely extended to an ℒ 2 -regular measure on the algebra generated by ℒ 2 . The case when ℒ 1 is not necessary contained in ℒ 2 , as well as the measure enlargement problem are considered. Furthermore, some discussions on normal lattices and separation of lattices are also given.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:723286

DOI: 10.1155/S0161171292000929

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