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I am looking at next semester's class schedule at my school, especially at a graduate course named Measure & Integration.

Officially it is described as "... an introduction to the principles, concepts and application of modern analysis. Topics include the Riemann integral, Lebesgue measure and integral, the Radon-Nikodym theorem, and applications to probability theory." Since it is a required course in all degree plans -- even for "light" concentration in math teaching, therefore I assume that it must be a basic course. However, when I scan the typical measure & integration textbooks, they generally require completion of at least one semester of real analysis as a prerequisite.

So here are my questions: (1) Is it possible to have a course in measure & integration without having completed real analysis? (PS. I am not totally clueless in various early topics in real analysis such as supremum and infimum, but I never took any real analysis class.) If it is possible, (2) I would love your suggestion to any textbook requiring little real analysis background, especially books with solutions/hints to the problem set. I would like to get ahead early by getting to know a little bit about it.

Thank you for your time and help.

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POST SCRIPT: I think I got what I am looking for, it is a book by Rene Schilling, Measure, Integrals & Martingales, Cambridge University Press. The author writes the book very informally, in down-to-earth style, he even maintains a blog listing the worked out solutions to the exercises here. Thank you for reading this posting.

A.Magnus
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  • I tend to recommend Bass's textbook for graduate students (specifically aimed at preparing grad students for prelim/qualifying exams). Make sure you know $\varepsilon-\delta$ definition of limit/continuity/differentiation and try to have a few examples on hand. As long as you're familiar with writing proofs, I think this is possible. One of big things you get out of that first analysis course is a nice set of counterexamples and an introduction to proof-writing. – Robert Cardona Nov 13 '14 at 16:40
  • @RobertCardona Awesome! Do you have any suggestion for texts that provide worked-out solutions or hints to their problem sets? Thanks again for your speedy response! – A.Magnus Nov 13 '14 at 16:52

1 Answers1

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To formalize my comment into an answer:

I tend to recommend Bass' textbook for graduate students which is aimed at preparing students for prelim/qualifying exams.

The prerequisites for this would be to make sure you know the $\varepsilon-\delta$ definition of limit/continuity/differentiation and try to have a few examples/counterexamples on hand.

As long as you are familiar with writing proofs, I think it could be possible; challenging, but possible. One of the big things you get out of that first analysis course is a nice set of examples/counterexamples and an introduction to proof writing.

The other recommendation, which has solved examples (which is another thing you were looking for) would beRene Schilling's, Measure, Integrals & Martingales which you mentioned in your post as a post script.

Robert Cardona
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