Measurable Functions and Topolgical Algebra

2023/08/29 by Geoff Vooys, Vooys, Geoff
Computer Science · Mathematics · #18C40 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 28E15 #Rings, Modules, and Algebras #Secondary 18C10

paper · pdf · doi:10.48550/arxiv.2308.15017

openalex publication_date 2023/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that if (X,A) is a measurable space and if Y is a topological model of a Lawvere theory T equipped with B the Borel σ-algebra on Y, then the set of B-measurable functions from X to Y, Meas(X,Y), is a set-theoretic model of T. As a corollary we give short proofs of the facts that the set of real-valued measurable functions on a measurable space X is a ring and the set of complex-valued measurable functions from X to ℂ is a ring.

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