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I'm self-studying from Measures, Integrals and Martingales. I find it good because the chapters are short and precise.

What is a good book to read to be well prepared to read Schilling's book? The pre-requisite book should cover some topics on rigorous analysis. The book should be as short and precise as Schiling's. I have bad experience with long books.

I have a Bachelor in Mathematical Economics from a Business School, so I know a lot about linear algebra and calculus but from an applied point of view ("understand the formulas and compute with parameters" approach). Now I try learn mathematical analysis from a theoretical point of view and am interested in books directed for pure math students.

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    $\begingroup$ Maybe a standard introduction to Real Analysis textbook such as Understanding Analysis by Abbot, or one of the many similar books. $\endgroup$
    – littleO
    Oct 8, 2017 at 11:41
  • $\begingroup$ How about Calculus, 4th edition, by Michael Spivak ? I taught a course based on that book. $\endgroup$
    – Albert
    Oct 8, 2017 at 11:46
  • $\begingroup$ @littleO I have looked at the first chapters of Understanding Analysis! That is indeed a good book. I will now read that before continuing to Schilling, Thanks! $\endgroup$
    – k.dkhk
    Oct 10, 2017 at 18:17

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Royden, real analysis. It's not short but it goes direct to the point, it's quite rigourous and definitely simple as a first reading. Moreover it would be very good for you since you don't have any topological background, and some basic facts are well presented in the text.

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  • $\begingroup$ My library has it so I would definitely have a look. By looking at the Content table, it seems that some topics of Schilling (which I referred to in my post) is covered in Boyden. Do you see Boyden as a replacement for Schilling or as a starting before moving on to Schilling? Thanks for your suggestion! $\endgroup$
    – k.dkhk
    Oct 8, 2017 at 15:03
  • $\begingroup$ My experience is Cohn: springer.com/gp/book/9781461469551 is a very nice book on measure theory and a much better choice for self-study than Schilling. $\endgroup$
    – g.s
    Oct 11, 2017 at 1:39
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This was already mentioned, but without a doubt, I would highly recommend Royden and Fitzpatrick's Real Analysis, 4th Edition for measure theory. It not only covers Lebesgue theory, but also general measure spaces. It introduces some basic concepts in the first chapter as well. You could also try Walter Rudin's Principles of Mathematical Analysis (Baby Rudin). It's a classic text which covers the Lebesgue theory in its last chapter. However, it is incredibly terse, so it may not be the best for beginners.

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    $\begingroup$ The 4th edition introduced a huge amount of errors in the text; I would use any other edition. $\endgroup$
    – Michael Greinecker
    Oct 11, 2017 at 4:34

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