Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.
We can compute (similarly as above)f(u)−f ′(u), and we obtain: 0 =f(u)−f ′(u) =f µ0 ·((P x∈X uµ0+[x])−u µ0), and sincef µ0 >0, it implies that P x∈X uµ0+[x] =u µ0
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Interpreting De Finetti's theorem in the Category of Integrable Cones (long version)
Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.