Hi, I just survived from a 1.5 year-long sequence in real analysis and measure-
theoretic probability. For me, the KSF to survive these high-level courses is
not simply hardworking but the ability to prove something in some creative ways
Many engineering PhD students sitting in these classes are for auditing only
because they don't have the time working on these homework assignments.
As these are usually PhD courses, your teacher will expect things more than
memorizing these theorems and results from you. Doing homeworks on these
courses at the same time can sometimes be a painstaking and insights-sharpening
process. It really takes time. And your math maturity really matters.
And...yes...from my experience the measure-theoretic probability is really
useful...if you want to learn more in stochastic analysis. The bottom line is
now I can read Karatzas & Shreve faster...1 page/hr.
My two cents.
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