TL;DR – go read this Probability Theory primer by Michael Betancourt https://betanalpha.github.io/assets/case_studies/probability_theory.html

I spent the past month or so struggling with the measure theoretic foundations of probability theory. What the heck are sigma algebras? Nothing I read really landed with the dozen or so brain cells I have dedicated to mathematics. You may rightly ask what could possible work with such little mental capacity.

From the shockingly limited learning I’ve somehow accomplished to date, I’ve made a couple far-reaching and likely false generalizations that fit my world view:

1) Every key insight can be explained simply given the correct framework.

2) Any esoteric notation or concept has an underlying motivation that can be simply explained.

My hope is that I can find those simple explanations for everything I care to learn. Sir Dr. Betancourt’s excellent exposition checked those boxes for me. Whether or not that translates into a workable grasp of these concepts is left to be determined.