A density version of a theorem of Banach

2024/11/17 by David A. Ross, Ross, David A.
Mathematics · #28A20 (Secondary) #28E05 (Primary) 26E35 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2411.11193

openalex publication_date 2024/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The S-measure construction from nonstandard analysis is used to prove an extension of a result on the intersection of sets in a finitely-additive measure space. This is then used to give a density-limit version of a representation theorem of Banach.

Related

• Open problems in Banach spaces and measure theory
• Density measures and additive property
• Density Properties of Sets in Finite-Dimensional, Strictly Convex Banach Spaces
• Support of Borelian Measures in Separable Banach Spaces
• Pure Measures, Density Measures and the Dual of L-infinity