Outer measures and associated lattice properties

Abstract

Zero-one measure characterizations of lattice properties such as normality are extended to more general measures. For a given measure, we consider two associated “outer” measures and attempt to obtain the “outer”-measurable sets. We also seek necessary and sufficient conditions for the measure and outer measures to be equal on the lattice or its complement.

Keywords

• measure
• lattice
• outer-measure
• measurable
• normal
• regular
• almost countably compact
• separates
• semiseparates
• support.