Borel selection of dominating hyperplanes

Eugenio Clerico

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arXiv · 2603.19973

Borel selection of dominating hyperplanes

Eugenio Clerico

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Abstract

We study a natural measurable selection problem for which the standard uniformisation theorems do not seem to apply directly, yet a Borel selector exists. More precisely, we consider families of finite dimensional functions that admit pointwise domination by affine functionals and ask whether such dominating functionals can be chosen in a Borel measurable way. We prove that this is indeed possible under semi-analytic regularity assumptions. The proof combines a one-dimensional Borel insertion result between an upper and a lower semi-analytic functions, derived from Lusin's separation theorem, with an induction on the dimension. As an application, we obtain Borel measurable selections of subgradients for parameter-dependent finite-dimensional convex functions, outside the scope of the standard normal integral framework.

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BibTeX RIS

Eugenio Clerico. 2026-03-20. Borel selection of dominating hyperplanes. https://arxiv.org/abs/2603.19973

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