[fyp]

I struggled through graduate analysis and measure theory as prereqs just to get to measure theoretic probability.

But I didn't retain much since it wasn't good for building intuition (informal proofs were better for that) and a lot of the corner cases it fixed didn't matter for the real world.

The language of measure theory makes a lot of proofs much shorter and easier to remember though. For example, markov's inequality: https://en.wikipedia.org/wiki/Markov%27s_inequality#In_the_l...