Darboux and shift-compactness paradigms: automatic continuity in the Gołąb-Schinzel and the Goldie equations

Ostaszewski, Adam ORCID: 0000-0003-2630-8663 (2025) Darboux and shift-compactness paradigms: automatic continuity in the Gołąb-Schinzel and the Goldie equations. Aequationes Mathematicae. ISSN 0001-9054

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Abstract

Using shift-compactness, the continuity theorems of Baire and Luzin and a variant of Darboux’s boundedness theorem, we deduce directly the continuity of positive solutions of the Gołąb-Schinzel equation and of the kernels of the closely related Goldie and generalized Goldie equation, from appropriate assumptions of the Baire property or (Lebesgue) measurability.

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	04 Aug 2025 09:03
Last Modified:	04 Nov 2025 17:43
URI:	http://eprints.lse.ac.uk/id/eprint/129006

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