On Alexandrov lattices

Albert Gorelishvili

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-11

Abstract:

By an Alexandrov lattice we mean a δ normal lattice of subsets of an abstract set X , such that the set of ℒ -regular countably additive bounded measures is sequentially closed in the set of ℒ -regular finitely additive bounded measures on the algebra generated by ℒ with the weak topology.

For a pair of lattices ℒ 1 ⊂ ℒ 2 in X sufficient conditions are indicated to determine when ℒ 1 Alexandrov implies that ℒ 2 is also Alexandrov and vice versa. The extension of this situation is given where T : X → Y and ℒ 1 and ℒ 2 are lattices of subsets of X and Y respectively and T is ℒ 1 − ℒ 2 continuous.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:218257

DOI: 10.1155/S0161171293000055

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