any suggestions for textbook or lectures on real analysis

Question

I had taken a course on calculus and read the first three chapters of amann's analysis（construction of the real number,convergence and continuous function）.But it's too late to start measure theory and integration,so I am looking for a good textbook or lecture note on real analysis.

Requirements:

1,the less theorems quoted from mathematics analysis,the better.(quoted theorems must be listed in the appendix)So stein and rudin are not in my choices.

2,modern.Like amann's style.And I've learned basic topology before.

3,(either one is okay) ①briefly introducing basic measure theory and integration for further topics(complex analysis and functional analysis). ②containing complete advanced topics,like lang's real and functional analysis.

Actually,I found bogachev’s real and functional analysis(springer's Moscow lecture) recently,but I am not sure it's suitable for me.Is there any prerequisite reading or learning I should do before embarking on reading this book?

Given to my background, what would be the best suggestions for real analysis texts?

Any suggestions are welcome,Thanks so much!

Answer 1

I recommend Royden's book "Real Analysis"

Answer 2

You might want to take a look at Measure, Integration & Real Analysis. The electronic version is legally available for free at https://measure.axler.net/, and the print version is reasonably priced.