What is Reddit's opinion of Measure, Integral and Probability?

From 3.5 billion Reddit comments

Roughly: Limits and the Riemann integral don't go well together. You can formulate some of the theorems for the Riemann integral but only under rather restrictive assumptions (high regularity of the functions involved). And then there is the completeness (every Cauchy sequence converges) of the L^p spaces, in particular the Hilbert space of QM.

But to actually calculate a Lebesgue integral you'll usually do this by calculating the Riemann integral (in case the function is Riemann integrable) or express it as a limit of Riemann integrals.

IMHO it's totally worth to learn Lebesgue integration, the fundamentals aren't that hard (this is a very gentle introduction). It's far easier to work with. And if you are interested in the mathematical foundations of QM or probability theory it's a must.