What books can fulfill the prerequisites to learn measure and integration theory?

Question

I'm self-studying from Measures, Integrals and Martingales. I find it good because the chapters are short and precise.

What is a good book to read to be well prepared to read Schilling's book? The pre-requisite book should cover some topics on rigorous analysis. The book should be as short and precise as Schiling's. I have bad experience with long books.

I have a Bachelor in Mathematical Economics from a Business School, so I know a lot about linear algebra and calculus but from an applied point of view ("understand the formulas and compute with parameters" approach). Now I try learn mathematical analysis from a theoretical point of view and am interested in books directed for pure math students.

Answer 1

Royden, real analysis. It's not short but it goes direct to the point, it's quite rigourous and definitely simple as a first reading. Moreover it would be very good for you since you don't have any topological background, and some basic facts are well presented in the text.

Answer 2

This was already mentioned, but without a doubt, I would highly recommend Royden and Fitzpatrick's Real Analysis, 4th Edition for measure theory. It not only covers Lebesgue theory, but also general measure spaces. It introduces some basic concepts in the first chapter as well. You could also try Walter Rudin's Principles of Mathematical Analysis (Baby Rudin). It's a classic text which covers the Lebesgue theory in its last chapter. However, it is incredibly terse, so it may not be the best for beginners.