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Lattice normality and outer measures. (English) Zbl 0759.28004
Summary: A lattice space is defined to be an ordered pair whose first component is an arbitrary set \(X\) and whose second component is an arbitrary lattice \(\mathcal L\) of subsets of \(X\). A lattice space is a generalization of a topological space. The concept of lattice normality plays an important role in the study of lattice spaces.
The present work establishes various relationships between normality of lattices of subsets of \(X\) and certain “outer measures” induced by measures associated with the algebras of subsets of \(X\) generated by these lattices.
MSC:
28A60 Measures on Boolean rings, measure algebras
28A12 Contents, measures, outer measures, capacities
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
54D99 Fairly general properties of topological spaces
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