Evan Misshula-From Outer Measures to Adjunctions: A CT Recasting of Caratheodory’s Extension Theorem
Автор: The New York City Category Theory Seminar
Загружено: 2025-12-04
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A talk given in The Graduate Center on December 3, 2025
Abstract: The Caratheodory Extension Theorem underpins modern measure theory by extending a pre-measure on an algebra to a complete measure on the generated -algebra. Traditionally, the proof proceeds through outer measures, Caratheodory measurability, and a series of delicate technical verifications – a process that reveals the "monsters" lurking in the power set but often obscures the structural simplicity of the result. In this talk, I will first outline the classical construction to highlight these subtleties, and then present a category-theoretic reformulation: the extension theorem emerges naturally from an adjunction. The categorical perspective streamlines the argument, but seeing both sides illuminates why rigor is indispensable and how category theory captures the essence of the construction.
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