A comprehensive book on graduate real analysis

Question

I'm looking for a comprehensive book/a comprehensive list of books on graduate analysis that covers/cover these topics: Lebesgue measure and integration on $\mathbb{R}^d$, the relationships between integrability and differentiability (it must also cover the theory of functions of bounded variation), complex analysis and fourier analysis.

Answer 1

The following books might be interesting in your case too:

• Mathematical Analysis (Apostol), since it covers Lebesgue measure and similar topics
• Real Analysis: A Comprehensive Course in Analysis, Part 1 (Berry Simon) is a very good reference too (I really like AMS books)
• A Passage to Modern Analysis (W. J. Terrell) is from AMS too and introduces things more gently (including Lebesgue measures) since it is from the series "Pure and Applied Undergraduate Texts"
• Manifolds and Differential Geometry (J. M. Lee) covers additionally smooth categories

The following books are available as PDF:

• Real Analysis (4th Ed.) by Royden
• Measure, Integration & Real Analysis (Open Access Book) by Sheldon Axler as already mentioned by Axion004
• Basic Analysis: Introduction to Real Analysis (free online textbook) by Jiří Lebl
• Basic Real Analysis (Stony Brook Mathematics)

Here is a chapter on Lebesgue Integral (the whole book Lectures on Real Analysis might be interesting, since one can see at least the chapter titles including descriptions of its content):

• The Lebesgue Integral