2014/10/31 by Tom Avery · 2 citations
Mathematics · Medicine · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #math.CT
paper · pdf · doi:10.1016/j.jpaa.2015.08.017
published as Journal of Pure and Applied Algebra, Volume 220, Issue 3, Pages 1229-1251 (2016) · 27 pages, final journal version
openalex publication_date 2015/09/03 · crossref created 2015/09/03 · crossref issued 2016/03/01 · crossref published 2016/03/01 · crossref published-print 2016/03/01 · arxiv created 2017/08/03 · arxiv updated 2017/08/04 · crossref deposited 2025/08/06 · crossref indexed 2025/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Giry monad on the category of measurable spaces sends a space to a space of all probability measures on it. There is also a finitely additive Giry monad in which probability measures are replaced by finitely additive probability measures. We give a characterisation of both finitely and countably additive probability measures in terms of integration operators giving a new description of the Giry monads. This is then used to show that the Giry monads arise as the codensity monads of forgetful functors from certain categories of convex sets and affine maps to the category of measurable spaces.