Lattice normality and outer measures.

*(English)*Zbl 0759.28004Summary: 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.

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 |