A universal construction adjoins infinite tensor products to FinStoch to produce a category of locally constant Markov kernels on finite sets union the Cantor space, enabling algebraic reasoning about continuous probability measures on the reals and lifting prior axiomatizations.
In: Bojańczyk, M., Simpson, A
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Approaching the Continuous from the Discrete: an Infinite Tensor Product Construction
A universal construction adjoins infinite tensor products to FinStoch to produce a category of locally constant Markov kernels on finite sets union the Cantor space, enabling algebraic reasoning about continuous probability measures on the reals and lifting prior axiomatizations.