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.
Annali di Matematica Pura ed Applicata29, 25–30 (1949),https://api.semanticscholar.org/CorpusID: 122252152
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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.