Hi,Which of these three books would you recommend as an introduction to measure theory:o First Look at Rigorous Probability Theory. Jeffrey S. Rosenthalo The Elements of Integration and Lebesgue Measure. Robert G. Bartleo Measure, Integral and Probability. Marek Capinski, Peter E. KoppBackground: my probability skills go as far as "Probability and Random Processes" by Grimmett and Stirzaker and my analysis skills are rather rudimentary.Thanks

Go first with Bartle to develop the mathematical foundation, which is measure theory, then continue with Capinski & Kopp. Afterward, for second reading and reference, you can read Patrick Billingsley's "Probability and Measure". If you want to take a shortcut or don't have enough time, just go straight with Capinski & Kopp. It has an accessible intro to measure theory. Well, it helped me get through an interview to Oxford's "Mathematical and Computational Finance" programme. But then again, I've read Bartle.

Thanks canis. I think I will take the shortcut and jump straight to Capinski & Kopp keeping in mind that I may need some background material.

Thank you quantmeh. Just got Karr's from the library. It is definitely quite gentle when it gets to presenting measure theory.

- moralExpectation
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Bartle is not particularly gentle but it is clear, complete and short. If you are happy motivating measure theory yourself then reading it and plowing through the exercises will give you a much better understanding than learning from a longer, slower book. If you become familiar with it it will serve well as a reference in the future.It is the reason I can do measure theory today and I thoroughly recommend it.

I am posting some references that present lebesgue integration and probability theory in terms of measure theory for engineers but without proofs. FYI, this is the way this is presented to students in France. It makes little sense in my opinion to go for a full-blown math approach unless you want to be a mathematician. For financial engineering and quant finance this whole topic is of relative value only. I find it much more modern and useful to approach stochastic processes from a (discrete-time) time series perspective rather than from a stochastic calculus perspective. Makes you much more marketable in the future. The reason the second approach has been so prominent is that complex derivatives were so hot and that is what everybody wanted to do.That is changing nowadays though. Anyway: these books are very very good.There is also:

- moralExpectation
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QuoteOriginally posted by: mtsmI find it much more modern and useful to approach stochastic processes from a (discrete-time) time series perspective rather than from a stochastic calculus perspective. Makes you much more marketable in the future. The reason the second approach has been so prominent is that complex derivatives were so hot and that is what everybody wanted to do.Sorry, I have no idea how you can claim that not understanding continuous processes case makes you more 'marketable'. You're talking about something fundamental to this field of maths, and absolutely central to mathematical finance. Avoiding learning something just because it's viewed as 'hard' will not make you more employable.

I am not suggesting that you not know about it. I am saying that it is possible to learn the language of measure theoretic probability by focusing on the results. There are works out there that will serve this up for you.The point you raise with the 'understanding' is interesting. So for you understanding means operating in a rigorous framework? That is one point of view.

- moralExpectation
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I wasn't objecting to the first part of your comment, that it was possible to learn the results without the proofs, although I don't necessarily agree.. I was taking issue with the second thing you said, which is that it better for a financial engineer to learn only discrete time processes without being able to work with continuous processes.

Knowing the results and understanding the language will get you quite far. It will let you read/decipher a lot of applied math literature. Not everybody has the time and energy to cover the whole material underlying in depth.Moreover many if not most people in this branch consider mathematics only a tool, so want to spend limited time on that.I am not saying that you should not spend any time on continuous time processes. I am saying that spending toomuch time focusing on intricate mathematical details, may mean not spending any time on other mathematical topicswhich receive too little attention typically.

- Cuchulainn
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I suppose Walter Rudin's books have gone out of fashion? And Schaum's Measure Theory.Awful dry stuff?

Last edited by Cuchulainn on August 30th, 2012, 10:00 pm, edited 1 time in total.

WIlliams - Probability with Martingales is my favourite probability book (including measure theory) and it's compactness means it is a good reference.

- NorwegianQuant
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Is there any book on measure theory for which it also exists a solution manual to the exercises ? In the book itself, in an additional book, or in a file available on the internet ...

- Cuchulainn
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This book is very good as a starters' text. It is clear, examples, exercises and solved problems. It discusses many topics up to 2nd year pure maths.It is certainly useful for understanding applications. Of course, there are more advanced texts like Rudin etc. but are drier and devoid of concrete examples. You need lots of examples and solutions precisely because the material is so non-intuitive and non-geometric. 221 course notes

Last edited by Cuchulainn on October 27th, 2012, 10:00 pm, edited 1 time in total.

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