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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.

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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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  • $\begingroup$ Thanks for the suggestion. However, I feel that these books are better suited as workbooks to complement a textbook, I would like solutions directly related to the book I'll be self-studying off of as they often make main ideas part of the exercises and I'd like to efficiently go through the main ideas before diving into the problems. $\endgroup$ – Charles C. Apr 20 '20 at 19:30
  • $\begingroup$ @CharlesC. Do you know DJVU format? it is for e-books. If you do not know it or you do not have it, just download it, it is free and so useful. I will provide a link for A VERY GOOD book, I will edit my answer. Check it, and please comment on the book. THANKS. $\endgroup$ – Hussain-Alqatari Apr 20 '20 at 19:45
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You will want to do multivariate calculus before doing Lebesgue Integration as certain topological principles are frequently used in the latter's development. . #2 will likely be difficult to find as the solution sets for math texts are generally not available to anyone but faculty.

There is a website, called Chegg, that has unofficial solutions to a large library of textbooks. I've just checked that the following one that I want to recommend is in fact on there:

An Introduction to Analysis, by Wade

Also, for Lebesgue Integration, the following is one of my favorite texts in all of mathematics.

A Primer of Lebesgue Integration, H.S. Bear

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I like Abbott's Understanding Analysis. Here is a website that suggests some texts at varying levels of denseness:

https://www.math.uh.edu/~tomforde/textbooks.html

In terms of working up to measure theory, here is the advice from my department chair when I tried to do a graduate independent study in measure theory:

"Make sure you have a solid understanding of abstract algebra, real analysis, and topology before taking measure theory. All three courses will help you immensely to prepare an understanding of the topics of measure theory but at the very least focus on abstract algebra and real analysis."

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