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arXiv · 2609.17851

A universal characterisation of the Bochner integral

Jean-David Jacques·Felix Medwed·Fabrizio Zanello
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Abstract

We provide a universal characterisation of the Banach spaces of equivalence classes of $L^p$ Bochner integrable functions, under equality almost everywhere, as initial objects in appropriate categories of bifunctors, for all $p \in [1,\infty)$. As a by-product of our construction, we also obtain a unique characterisation of the Bochner integral.

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Jean-David Jacques, Felix Medwed, Fabrizio Zanello. 2026-09-15. A universal characterisation of the Bochner integral. https://arxiv.org/abs/2609.17851

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