This is will be an expository talk, explaining the work of Rafael Sorkin of the Perimeter Institute.

arXiv:gr-qc/9401003 Kolmogorov’s axioms give the correct formulation of probability for classical physics. But quantum probabilities do not satisfy the axiom P(A\cup B)=P(A)+P(B)-P(A\cap B). This is the phenomenon of “quantum interference” or “quantum entanglement”. Sorkin has suggested an axiom that replaces it, which has been experimentally verified to hold in quantum mechanics. Remarkably, he found that it is the first of a sequence of generalizations of classical measure theory. Even if the further generalizations are not currently needed in physics, they might be worth investigating mathematically.