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<p>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.</p>

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

  • 期刊论文

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  • 发表日期：

    2025年9月15日

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  • Adam J. Ostaszewski

摘要

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.