Darboux and shift-compactness paradigms: automatic continuity in the Gołąb-Schinzel and the Goldie equations
Ostaszewski, A.
(2025).
Darboux and shift-compactness paradigms: automatic continuity in the Gołąb-Schinzel and the Goldie equations.
Aequationes Mathematicae,
99(6), 2819 - 2845.
https://doi.org/10.1007/s00010-025-01209-x
(2025).
Darboux and shift-compactness paradigms: automatic continuity in the Gołąb-Schinzel and the Goldie equations.
Aequationes Mathematicae,
99(6), 2819 - 2845.
https://doi.org/10.1007/s00010-025-01209-x
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.
