2019/02/15 by Svetlana V. Butler, Butler, Svetlana V.
Mathematics · #28A25 #28C05 #28C15 (Secondary) #46G99 (Primary) 46E27 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.1902.05692
openalex publication_date 2019/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study non-linear functionals, including quasi-linear functionals, p-conic\nquasi-linear functionals, d-functionals, r-functionals, and their relationships\nto deficient topological measures and topological measures on locally compact\nspaces. We prove representation theorems and show, in particular, that there is\nan order-preserving, conic-linear bijection between the class of finite\ndeficient topological measures and the class of bounded p-conic quasi-linear\nfunctionals. Our results imply known representation theorems for finite\ntopological measures and deficient topological measures. When the space is\ncompact we obtain four equivalent definitions of a quasi-linear functional and\nfour equivalent definitions of functionals corresponding to deficient\ntopological measures.\n