Any suggestions about good Analysis Textbooks that covers the following topics?

manpreet Best Answer 3 years ago

I am an undergraduate math major student. I took two courses in Advanced Calculus (Real Analysis): one in Single variable Analysis, and the second in Multivariable Analysis. We basically used Rudin's Book "Principles of Mathematical Analysis" as a textbook, and we covered the first 9 chapters of the book(Namely: 1. Real and Complex Number Systems. 2- Basic Topology. 3-Numerical Sequences and Series. 4- Continuity. 5- Differentiation. 6- Riemann-Stieltjes Integral. 7- Sequences and Series of Functions. 8- Some special Functions. 9-Functions of several variables).

I am looking for a good (and easy to read) textbook, preferably with many examples (or solved problems) that covers the following topics:

• algebras and measures;
• the measure theoretic integral (in particular, the N-dimensional Lebesgue integral);
• convergence theorems;
• product measures;
• absolute continuity;
• signed measures;
• the Lebesgue-Stieltjes integral.

This is also another description of the topics covered that I found on the syllabus of the course: "Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on RnRn, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions"

I appreciate any kind of suggestion about a good textbook that I can use to learn the topics above by self-study. I prefer if you can tell me about the easy-to-read ones with examples and solved problems, because it's very hard for me to understand analysis without solving examples and problems. Thanks in advance for the help!

manpreet 3 years ago