Pré-Publication, Document De Travail Année : 2025

Projective functions

Résumé

We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums, differences, products, finite suprema and infima, sections and compositions. Assuming the set-theoretical axiom of Projective Determinacy, we also prove measurable selection results, stability under integration, and the existence of epsilon-optimal selectors. Finally, we illustrate how these results are important in the context of model uncertainty.

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Dates et versions

hal-05139854 , version 1 (02-07-2025)

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  • HAL Id : hal-05139854 , version 1

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Laurence Carassus, Massinissa Ferhoune. Projective functions. 2025. ⟨hal-05139854⟩
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