> To the extent that one doesn’t need measure theory to do statistical mechanics there is no need to teach measure theory in a statistical mechanics course. I

> To the extent that one doesn’t need measure theory to do statistical mechanics there is no need to teach measure theory in a statistical mechanics course. I never assumed otherwise. That being said, I couldn't be bothered to memorize and reproduce the handwavy exposition that made sense to a particular physicist. And it's not that I was there to prove a point - I was asked about the basic constructions like probability distributions, densities etc. > infinite sets, measure theory, and mathematical pathology > By the way, rigour and generality are different things. Measure theory and Kolmogorov axiomatization addressed very real problems like Bertrand's paradox plaguing classical probabilit to the point that it was often seen as a black art rather than science. Moreover, stochastic processes in continuous time are not very intuitive and a sound theory would be next to impossible to develop without solid foundations.