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I bought the fourth edition of Royden Real Analysis, this book is awesome and it's quite different from the third edition, which has less exercises.

I have the solution manual for the third edition. Is there a solution manual for the fourth edition?

I always like doing the exercises by myself, but it is very important for me to be able to verify that they are correctly solved.

Cristian Baeza
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Gaston Burrull
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2 Answers2

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This book is such a gem! As a hobby, I've been writing up solutions to the exercises in my free time. You can download them from my website. I've only managed to make it through Chapter 8 though.

I hope you find these useful - my only request is to please let me know if you find any errors :-)

David
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    thank you very much, it is not going to be useful for me after that many years, but surely someone will find very useful your answer :) – Gaston Burrull Sep 28 '20 at 07:03
  • I’m not sure this is a mistake but maybe something I would like more info about. In section 2.3 problem 15 on page 38 you use countable additivity but this property is not proven until section 2.5. I don’t think your proof is wrong, but I’m inclined to think that there is an alternative that only uses countable sub-additivity. – ToucanIan Jan 30 '22 at 03:24
  • @ToucanIan Thanks for the feedback! I updated the solution to that exercise. – David Feb 06 '22 at 23:50
  • In section 2.4 problem 18 you appear to make the assumption that E is measurable. In my version of the text E is simply stated to have a finite measure but is not said to be measurable. – ToucanIan Feb 07 '22 at 20:13
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    Yeah I agree the language a little ambiguous. I believe "finite measure" implies the set is measurable, in contrast with the term "finite outer measure" (e.g. exercise 14). It doesn't make much sense to say a set's measure is finite if the set is not measurable. – David Feb 08 '22 at 15:06
  • My version of the text explicitly says “finite outer measure” I did not correctly relay this in the original comment. Sorry for the confusion. – ToucanIan Feb 21 '22 at 17:32
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Here is a solutions manual through Chapter 16 of the 2018 reissue of the fourth edition: https://www.amazon.com/dp/B0DNCMTT31.

user0
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