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Mathematics > Category Theory

arXiv:1803.07956 (math)
[Submitted on 21 Mar 2018 (v1), last revised 3 Sep 2018 (this version, v2)]

Title:A note on $σ$-algebras on sets of affine and measurable maps to the unit interval

Authors:Tomas Crhak
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Abstract:In The factorization of the Giry monad (arXiv:1707.00488v2) the author considers two $\sigma$-algebras on convex spaces of functions to the unit interval. One of them is generated by the Boolean subobjects and the other is the $\sigma$-algebra induced by the evaluation maps. The author asserts that, under the assumptions given in the paper, the two $\sigma$-algebras coincide. We give examples contradicting this statement.
Comments: 5 pages
Subjects: Category Theory (math.CT)
Cite as: arXiv:1803.07956 [math.CT]
  (or arXiv:1803.07956v2 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.1803.07956

Submission history

From: Tomas Crhak [view email]
[v1] Wed, 21 Mar 2018 15:03:29 UTC (5 KB)
[v2] Mon, 3 Sep 2018 15:30:05 UTC (5 KB)
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