[Math] Looking for a Real Analysis textbook with solutions for self study

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I am wondering if there are any good texts out there that also have a solution easily available.

I've found solutions to Mathematical Analysis by Apostol and Principles of Mathematical Analysis by Rudin but found them a bit too dense for my background (single-variable calculus with an emphasis on theory/proofs instead of application). I also came across Understanding Analysis by Abbott but I'd prefer something that covers a more extensive range of topics (like that of the first two). I might be asking for too much but is there a book that:

  1. Has a good exposition of the content (I'd prefer more hand-holding over less)

  2. Has solutions either online (not necessarily by the auther of the book) or in the back of the book

  3. Covers more content like Lebesgue Integrals or perhaps Multivariable Calculus

My initial plan was to go with Understanding Analysis since it covers 1) and 2) but then I'd face the issue with finding the same characteristics in a book that picks up where Understanding Analysis left off as most textbooks don't have easily accessible solutions which I find incredibly useful especially since I'll be self-studying.

Best Answer

I can recommend you two books. They are old (1990 & 1974), but I believe they are (SO SO) awesome.

FIRST:

Problems in Real Analysis - A Workbook with Solutions

Charalambos D. Aliprantis, Owen Burkinshaw

Academic Press

1990

SECOND:

Exercises in Real and Complex Analysis with Solutions

Walter Rudin

1974

Also, here a book with (DJVU) format:

DOWNLOAD

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