Could someone reccommend me an appropriate book please?

I've just completed an introductory analysis course (covered the real numbers, sequences & series, basic topology of R, functional limits & continuity, derivatives, sequences & series of functions, introduction to metric spaces). I've also taken courses in probability and random processes, which I greatly enjoyed, but I've never looked at it from a measure-theoretic approach... now I'm wanting to move into a more rigourous treatment of the subject.

I'll be self-studying this, so ideally the book would have some exercises with worked solutions, but if it only has a decent selection of worked examples in the main text that would be OK too.

It needs to be an introductory text - it can't assume any knowledge of analysis beyond what I wrote up there^... But, at the same time I'd like to learn the subject rigorously, - no hand wavy intuitive 'proofs'... I want the proper stuff... I'm not sure if "introductory" and "graduate level" are mutually exclusive, but if not I want both...

Above all, an emphasis on explanation of ideas (hand wavy intuitive proofs are a very welcome complement to the technical proofs!), and discussion of consequences, - examples, etc... is paramount.


Has anyone ever used this book: Amazon.com: Measure, Integral and Probability: Marek Capinski, Peter E. Kopp: Books

? It sounds like exactly what I want, but I don't trust the reviews on Amazon.


Thanks to anyone that helps me!

Hi,

I've had glances at this book. It looks interesting. I even planned to borrow it in order to learn again measure theory (since I don't think I learnt seriously lol). What I like in it, and what should fit for you, is that there are parts in almost every chapter that explain how what you've just been reading about measure theory will relate to probability.

Well, it's worth trying in my opinion

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Great, thanks!

Hey Aileys,

I started a course on integration and measure theory last term and the Capinski & Copp book is a very good text. I also strongly recommend Introduction to Integration, H.A Priestley. It can be rather hard at times but overall is a very clear, comprehensive and rewarding text with lots of worked examples and further theory.

http://books.google.co.uk/books?id=H...snum=1#PPP1,M1

Hope this helps.