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it's particularly popular that one in all Hilbert’s recognized checklist of difficulties is that of constructing an axiomatic idea of mathematical chance conception (this challenge can be acknowledged to were solved by means of Khintchine, Kolmogorov, and
Levy), and in addition one of the checklist is the “axiomatization of physics.” what's no longer so renowned is that those are components of 1 and an identical challenge, specifically, the 6th, and that the axiomatics of chance are mentioned within the context of the principles of statistical mechanics. even supposing Hilbert couldn't have identified it while he formulated his difficulties, chance concept can also be valuable to the rules of quantum idea. during this booklet, I desire to describe a truly varied interface among chance and mathematical physics, particularly, using yes notions of integration in functionality areas as technical instruments in quantum physics. even if Nelson has proposed a few connection among those notions and foundational questions, we will deal completely with their use to reply to various questions in
conventional quantum theory.

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