Lebesgue Integral - Self Learning

Question

I finished some courses on Calculus at college sometime ago, then it goes without saying I learned Riemann Integrals. However, I realized that there is another type of integrating functions: Lebesgue Integrals. Because of this, I really would like to understand them by my own.

Which books would you recommend for me, who wants to learn by my on during this quarantine. It would be nice if the book contained exercises or even were like Stewart's Calculus.

Thank you

Answer 1

I will answer the question, but first I'd like to say that if you really are operating at the level of rigor of Stewart's calculus book (as opposed to more advanced calculus or analysis books that emphasize proofs), it seems unlikely to me that you'll find learning the details of Lebesgue integration feasible or useful.

With that reservation, I can recommend either of the following two concise introductions: - Bartle, The Elements of Integration and Lebesgue Measure. - Burkill, The Lebesgue Integral.

Incidentally, Burkill is also the author of A First Course in Mathematical Analysis and A Second Course in Mathematical Analysis. The first of these would likely provide sufficient background for studying his book on the Lebesgue integral.

Answer 2

I reccomend you :

-A Radical Approach to Lebesgue's Theory of Integration

-The Integrals of Lebesgue, Denjoy, Perron, and Henstock

The only prerequisite is elementary real analysis.