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arXiv · 2307.01788

A Radon-Nikod\'ym Theorem for Valuations

Jean Goubault-Larrecq
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Abstract

We enquire under which conditions, given two $\sigma$-finite, $\omega$-continuous valuations $\nu$ and $\mu$, $\nu$ has density with respect to $\mu$. The answer is that $\nu$ has to be absolutely continuous with respect to $\mu$, plus a certain Hahn decomposition property, which happens to be always true for measures.

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Jean Goubault-Larrecq. 2023-07-04. A Radon-Nikod\'ym Theorem for Valuations. https://arxiv.org/abs/2307.01788

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