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Many of the really good introduction-type books have already been mentioned. As a current grad student I encounter many of them on an almost daily basis and would suggest the following:

  • Billingsley - "Probability and measure", although I would skip the first part about the dyadic intervals.

  • Durrett - "Probability: Theory and examples". I used the 3rd version when I was taught from this book and then it did not have that much measure theory in the, sense that it was confined to the appendix. As I understand it this is not the case for the 4th edition and I really love the way Durrett presents the material so this is a good starting point.

  • Shiryayev - "Probability". Great book from one of the current masters. It starts with an intuitive discussion about probability theory and then moves on to develop the mathematical theory needed (sample spaces and so on) in order to "do real probability". I haven't read the entire thing so that's why I can't put this as my #1 choice, I seems as if it has the potential though.

  • Williams - "Probability with martingales". Very nicely written account of measure theoretic probability. It is quite concise though and depending on your mathematical maturity it could perhaps be a bit difficult to follow completely. One possibility is to keep the author's "Weighing the odds" at your side to get the elementary theory as a complement to the more advanced book.

  • Feller - There is a reason why it's called considered a classic.

Another, perhaps somewhat odd and unconventional, choice might also be Tomas Björk - "Arbitrage theory in continuous time". Now it's not an introduction to probability but depending on what type of economics you are interested this could be a nice reference book. It has an appendix devoted to measure theory and probability and Prof. Björk being one of the best teachers I've had in terms of providing you with an intuitive feeling for the subject at hand, I'm sure that such sections would work very well for someone who is just trying to get a basic understanding of the subject.
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Many of the really good introduction-type books have already been mentioned. As a current grad student I encounter many of them on an almost daily basis and would suggest the following:

  • Billingsley - "Probability and measure", although I would skip the first part about the dyadic intervals.

  • Durrett - "Probability: Theory and examples". I used the 3rd version when I was taught from this book and then it did not have that much measure theory in the, sense that it was confined to the appendix. As I understand it this is not the case for the 4th edition and I really love the way Durrett presents the material so this is a really good starting point.

  • Shiryayev - "Probability". Great book from one of the current masters. It starts with an intuitive discussion about probability theory and then moves on to develop the mathematical theory needed (sample spaces and so on) in order to "do real probability". I haven't read the entire thing so that's why I can't put this as my #1 choice, I seems as if it has the potential though.

  • Williams - "Probability with martingales". Very nice nicely written account of measure theoretic probability. It is quite concise though and depending on your mathematical maturity it could perhaps be a bit difficult to follow completely. One possibility is to keep the author's "Weighing the odds" at your side to get the elementary theory as a complement to the more advanced book.

  • Feller - There is a reason why it's called a classic.

Another, perhaps somewhat odd and unconventional, choice might also be Tomas Björk - "Arbitrage theory in continuous time". Now it's not an introduction to probability but depending on what type of economics you are interested this could be a nice reference book. It has an appendix devoted to measure theory and probability and Prof. Björk being one of the best teachers I've had in terms of providing you with an intuitive feeling for the subject at hand, I'm sure that such sections would work very well for someone who is just trying to get a basic understanding of the subject.
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Many of the really good introduction-type books have already been mentioned. As a current grad student I encounter many of them on an almost daily basis and would suggest the following:

  • Billingsley - "Probability and measure", although I would skip the first part about the dyadic intervals.

  • Durrett - "Probability: Theory and examples". I used the 3rd version when I was taught from this book and then it did not have that much measure theory in the sense that it was confined to the appendix. As I understand it this is not the case for the 4th edition and I really love the way Durrett presents the material so this is a really good starting point.

  • Shiryayev - "Probability". Great book from one of the current masters. It starts with an intuitive discussion about probability theory and then moves on to develop the mathematical theory needed (sample spaces and so on) in order to "do real probability". I haven't read the entire thing so that's why I can't put this as my #1 choice, I seems as if it has the potential though.

  • Williams - "Probability with martingales". Very nice written account of measure theoretic probability. It is quite concise though and depending on your mathematical maturity it could perhaps be a bit difficult to follow completely. One possibility is to keep the author's "Weighing the odds" at your side to get the elementary theory as a complement to the more advanced book.

  • Feller - There is a reason why it's called a classic.

A

Another, perhaps somewhat odd and unconventional, choice might also be Tomas Björk - "Arbitrage theory in continuous time". Now it's not an introduction to probability but depending on what type of economics you are interested this could be a nice reference book. It has an appendix devoted to measure theory and probability and Tomas Prof. Björk being one of the best teachers I've had in terms of providing you with an intuitive feeling for the subject at hand, I'm sure that such sections would work very well for someone who is just trying to get an a basic understanding of the subject. I am not intimately familiar with the book (I am not doing research in that field) but as I understand it, it is almost required reading for anyone who is serious about mathematical finance.
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