Snow Zhang (NYU)

The Borel-Kolmogorov paradox is the phenomenon that, sometimes, when P(E) = 0, the probability of H given E appears to depend on the specification of the sigma algebra from which E is drawn. One popular diagnosis of the paradox is that it reveals a surprising fact about conditional probability: when P(E) = 0, the value of P(H|E) depends on the choice of a sigma algebra. As Kolmogorov himself put it, “[the paradox shows that] the concept of a conditional probability with regard to an isolated given hypothesis whose probability equals 0 is inadmissible” (p.51, 1956).