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On subadditive functions bounded above on a large set

Bingham, N. H., Jabłońska, Eliza, Jabłoński, Wojciech and Ostaszewski, Adam (2020) On subadditive functions bounded above on a large set. Results in Mathematics, 75 (2). ISSN 1422-6383

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Identification Number: 10.1007/s00025-020-01186-4

Abstract

It is well known that boundedness of a subadditive function need not imply its continuity. Here we prove that each subadditive function f: X→ R bounded above on a shift–compact (non–Haar–null, non–Haar–meagre) set is locally bounded at each point of the domain. Our results refer to results from Kuczma’s book (An Introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality, 2nd edn, Birkhäuser Verlag, Basel, 2009, Chapter 16) and papers by Bingham and Ostaszewski [Proc Am Math Soc 136(12):4257–4266, 2008, Aequationes Math 78(3):257–270, 2009, Dissert Math 472:138pp., 2010, Indag Math (N.S.) 29:687–713, 2018, Aequationes Math 93(2):351–369, 2019).

Item Type: Article
Official URL: https://www.springer.com/journal/25
Additional Information: © 2020 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 16 Mar 2020 10:42
Last Modified: 14 Jul 2020 08:39
URI: http://eprints.lse.ac.uk/id/eprint/103762

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