So here am I studying probability theory. I am already presented to the basics, which means that I am acquainted to most of the theory proposed by Sheldon Ross' book "A First Course in Probability". Although I am very pleased at reading it, I would like to receive some suggestion of bibliography involving measure theory (for statisticians). Can anyone provide me a title? Thanks in advance.

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    $\begingroup$ Related thread (though not exactly what you're looking for): math.stackexchange.com/questions/315075/… Folland is another book to be aware of; it's a popular textbook on measure theory that includes a chapter on probability. Durrett's probability textbook is good. $\endgroup$ – littleO Jan 10 at 3:10
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    $\begingroup$ @littleO: Do you mean "Probability: Theory and Examples"? The book is a good read but I it would be a little heavy for a first approach to measure theory. $\endgroup$ – copper.hat Jan 10 at 3:25
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    $\begingroup$ @copper.hat Yes, that's the one, and I agree it would be a little heavy. I also think that Folland isn't the easiest introduction to measure theory. I'll be interested to see other suggestions. $\endgroup$ – littleO Jan 10 at 3:28
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    $\begingroup$ Ross' Second Course in Probability is a fairly friendly introduction to measure-theoretic probability. There's also Billingsley's Probability and Measure, which is an excellent but difficult text. $\endgroup$ – David Kraemer Jan 10 at 14:38
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    $\begingroup$ This is not really a suggestion, but Kingman and Taylor's Introdction to Measure and Probability may worth a look. It's a bit dry, but on my first read I was pleasantly surprised that it cares to explain how to construct a product topology for infinitely many topological spaces. This should be a piece of useful and basic knowledge, but for some unknown reason, many textbooks only discuss finite products. So, while I have never seriously delved into it, I still remember this book to this date. $\endgroup$ – user1551 Jan 13 at 22:01

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