TL;DR
This paper proves that the set of all measures on any measurable space forms a complete lattice, meaning every collection of measures has well-defined supremum and infimum, which is fundamental for measure theory.
Contribution
It establishes that measures on any measurable space form a complete lattice, providing a foundational structure for measure theory and related mathematical fields.
Findings
The set of all measures is a complete lattice.
Every collection of measures has a greatest lower bound.
Every collection of measures has a least upper bound.
Abstract
We show that the set of all measures on any measurable space is a complete lattice, i.e. every collection of measures has both a greatest lower bound and a least upper bound.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topology and Set Theory