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In The factorization of the Giry monad (arXiv:1707.00488v2) the authorconsiders two $\sigma$-algebras on convex spaces of functions to the unitinterval. One of them is generated by the Boolean subobjects and the other isthe $\sigma$-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.

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