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Automatic continuity: subadditivity, convexity, uniformity

Bingham, N. H. and Ostaszewski, A. J. (2009) Automatic continuity: subadditivity, convexity, uniformity. Aequationes Mathematicae, 78 (3). pp. 257-270. ISSN 0001-9054

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Identification Number: 10.1007/s00010-009-2982-x


We examine various related instances of automatic properties of functions – that is, cases where a weaker property necessarily implies a stronger one under suitable side-conditions, e.g. connecting geometric and combinatorial features of their domains. The side-conditions offer a common approach to (mid-point) convex, subadditive and regularly varying functions (the latter by way of the uniform convergence theorem). We consider generic properties of the domain sets in the side-conditions – properties that hold typically, or off a small exceptional set. The genericity aspects develop earlier work of Kestelman [Kes] and of Borwein and Ditor [BoDi]. The paper includes proofs of three new analytic automaticity theorems announced in [BOst7].

Item Type: Article
Official URL:
Additional Information: © 2009 Birkhäuser Verlag, Basel
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Date Deposited: 31 Mar 2010 13:37
Last Modified: 03 Apr 2024 04:30

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