Advice on (my) Measure Theory book choice needed

Question

I just finished by measure theory course and I feel the need to really solidify my limited knowledge as I am not happy with the final marks I was able to get.

I did some research online and arrived at the following book choices in reading order, I would like some advice/recommendations on whether my choice of books is appropriate or not.

My knowledge on this subject is fairly limited and I do have a very simplistic understanding on most topics. I decided to start right from the beginning. Here are the books I decided to add to my reading list:

1. Lebesgue Integration on Euclidean Space, Revised Edition (Jones and Bartlett Books in Mathematics) -- Frank Jones
2. Real Analysis -- Royden
3. Real and Complex Analysis -- Rudin
4. Real Analysis: Modern Techniques and Their Applications -- Folland

I am also thinking of picking up a copy of "Functional Analysis" by Rudin. Would it be necessary to get the Royden book (listed above) along with the Rudin one, or is the Rudin one enough? Are there any better alternatives worth looking into?

Any advice is appreciated, thanks!

Answer 1

You can follow Real analysis by Stein and Shakarchi. Book gives measure theory description with the use of cubical covering makes it very intuitive.

Answer 2

I recommend A User-Friendly Introduction to Lebesgue Measure and Integration.