I am learning measure theory from Papa Rudin. I am just trying to capture the ideas conceptually. First of all, how far is measurable sets from topological sets.
I guess this question could be phrased as can we generate more complex subsets of a set $X$ using the conditions of measurable sets than conditions of topological sets.
Secondly, the book explains that what lead to the abstract theory of integration was that normal Riemann integral couldn’t deal with limits. Can someone explain that more ?