While Kolmogorov's definition of probability looks a bit spooky at first, I definitely recommend going through it at some point. Not only it feels nice, it also

While Kolmogorov's definition of probability looks a bit spooky at first, I definitely recommend going through it at some point. Not only it feels nice, it also makes understanding probabilistic concepts easier (e.g. understanding that a statistical space is simply a "lifted", or rather parametrized, version of a probabilistic space).