I'm currently studying measure-theoretic probability and have so far learned until generated sigma-algebras and Borel sets/sigma-algebra. As I understand it, measure theory helps unify a lot of the "discrete vs continuous" subjects in undergraduate probability. What are some specific examples of such unification?

  • $\begingroup$ using measure theory, you can deal with mixed random variables too, also it removes the almost surely notation. Two examples out of many on how this is useful. $\endgroup$ – P. Quinton Feb 19 at 10:10

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