Author:
Bingham Nicholas H.,Jabłońska Eliza,Jabłoński Wojciech,Ostaszewski Adam J.
Abstract
AbstractIt is well known that boundedness of a subadditive function need not imply its continuity. Here we prove that each subadditive function $$f:X\rightarrow {\mathbb {R}}$$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).
Funder
Pedagogical University of Cracow
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
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