Level Sets and the Uniqueness of Measures

DOI10.1112/JLMS/S2-48.2.249zbMATH Open0790.28001arXivmath/9201223OpenAlexW2107214616MaRDI QIDQ4286377

Dale Alspach

Publication date: 27 April 1994

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Abstract: A result of Nymann is extended to show that a positive $sigma$-finite measure with range an interval is determined by its level sets. An example is given of two finite positive measures with range the same finite union of intervals but with the property that one is determined by its level sets and the other is not.

Full work available at URL: https://arxiv.org/abs/math/9201223

zbMATH Keywords

extreme pointsrangelevel setsfinite positive measures

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Real- or complex-valued set functions (28A10)

Related Items (4)

Conditions for the finiteness of the moments of the volume of level sets ⋮ Level sets lemmas and unicity of critical point of invariants, tools for local stability and topological properties of dynamical systems ⋮ Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets ⋮ Sofic Measures and Densities of Level Sets

Recommendations

• Measure-theoretic properties of level sets of distance functions 👍 👎
• Finiteness of Hausdorff measure of level sets of bounded subsets of Euclidean space 👍 👎
• Level sets of Hölder functions and Hausdorff measures. 👍 👎
• Sofic Measures and Densities of Level Sets 👍 👎
• Hausdorff Measure and Level Sets of Typical Continuous Mappings in Euclidean Spaces 👍 👎
• Level sets of depth measures in abstract spaces 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎

This page was built for publication: Level Sets and the Uniqueness of Measures

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4286377)