A note on $\sigma$-algebras on sets of affine and measurable maps to the unit interval

Tomas Crhak

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arXiv · 1803.07956

A note on $\sigma$-algebras on sets of affine and measurable maps to the unit interval

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.

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BibTeX RIS

Tomas Crhak. 2018-03-21. A note on $\sigma$-algebras on sets of affine and measurable maps to the unit interval. https://arxiv.org/abs/1803.07956

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