This is a rephrase of the questions posted regarding measure theory but also including integration. (Reference book on measure theory)
I have to review the knowledge of measure and integration theories for the sake of continue the work that I started in my thesis.
I am not totally new with axiomatic measure theory and integration theory, I have some knowledge due to self-study. Now I feel that all the knowledge has gone and still don’t have a clear overview on the structure of measure and integration theories. And here come my specified requirements for a reference book.
I wish the book elaborates the proofs, since I will read it on my own again, sadly. And this is the most important criterion for the book.
I wish the book covers most of the topics in measure and integration theories. I do want to review both theories at a more general level. If such a condition cannot be achieved, I'd like to more focus on integration.
I wish the book could deal with convergences and uniform integrability carefully.
My expectation is after thorough reading, I could have strong background on measure and integration at an analytic level.
Sorry for such a tedious question.