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Zach N
Zach N
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Well,I I personally HATE Halmos' Measure Theory  , even though an entire generation grew up on it. My favorite book on measure and integration is available in Dover paperback and is one of my all time favorite analysis texts: Angus Taylor's General Theory Of Functions And Integration. Lots of wonderful examples and GREAT exercises along with discussions of point set topology,measure measure theory both on R$\mathbb{R}$ and in abstract spaces and the Daneill approach. And all written by a master analyst with lots of references for further reading.It's It's one of my all time favorites and I heartily recommend it. Folland's Real Analysis is a fine book,but but it's much harder and it's really more of a general first year graduate analysis course. OnOn the plus side,it it does have many applications,including probabiliy including probability and harmonic analysis. It's definitely worth having,but but it's going to take a lot more effort then Taylor.The The IDEAL thing to do would be to work through both books simultaneously for a fantastic course in first year graduate analysis. And please don't torture yourself with Rudin's Real And Complex Analysis. It's sole purpose seems to be to see how much analysis can be crammed incomprehensibly into a single text. Folland is the same level and is much more accessible. That should get you started.Good Good luck!

Well,I personally HATE Halmos' Measure Theory  , even though an entire generation grew up on it. My favorite book on measure and integration is available in Dover paperback and is one of my all time favorite analysis texts: Angus Taylor's General Theory Of Functions And Integration. Lots of wonderful examples and GREAT exercises along with discussions of point set topology,measure theory both on R and in abstract spaces and the Daneill approach. And all written by a master analyst with lots of references for further reading.It's one of my all time favorites and I heartily recommend it. Folland's Real Analysis is a fine book,but it's much harder and it's really more of a general first year graduate analysis course. On the plus side,it does have many applications,including probabiliy and harmonic analysis. It's definitely worth having,but it's going to take a lot more effort then Taylor.The IDEAL thing to do would be to work through both books simultaneously for a fantastic course in first year graduate analysis. And please don't torture yourself with Rudin's Real And Complex Analysis. It's sole purpose seems to be to see how much analysis can be crammed incomprehensibly into a single text. Folland is the same level and is much more accessible. That should get you started.Good luck!

Well, I personally HATE Halmos' Measure Theory, even though an entire generation grew up on it. My favorite book on measure and integration is available in Dover paperback and is one of my all time favorite analysis texts: Angus Taylor's General Theory Of Functions And Integration. Lots of wonderful examples and GREAT exercises along with discussions of point set topology, measure theory both on $\mathbb{R}$ and in abstract spaces and the Daneill approach. And all written by a master analyst with lots of references for further reading. It's one of my all time favorites and I heartily recommend it. Folland's Real Analysis is a fine book, but it's much harder and it's really more of a general first year graduate analysis course. On the plus side, it does have many applications, including probability and harmonic analysis. It's definitely worth having, but it's going to take a lot more effort then Taylor. The IDEAL thing to do would be to work through both books simultaneously for a fantastic course in first year graduate analysis. And please don't torture yourself with Rudin's Real And Complex Analysis. It's sole purpose seems to be to see how much analysis can be crammed incomprehensibly into a single text. Folland is the same level and is much more accessible. That should get you started. Good luck!

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The Mathemagician
The Mathemagician
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Well,I personally HATE Halmos' Measure Theory , even though an entire generation grew up on it. My favorite book on measure and integration is available in Dover paperback and is one of my all time favorite analysis texts: Angus Taylor's General Theory Of Functions And Integration. Lots of wonderful examples and GREAT exercises along with discussions of point set topology,measure theory both on R and in abstract spaces and the Daneill approach. And all written by a master analyst with lots of references for further reading.It's one of my all time favorites and I heartily recommend it. Folland's Real Analysis is a fine book,but it's much harder and it's really more of a general first year graduate analysis course. On the plus side,it does have many applications,including probabiliy and harmonic analysis. It's definitely worth having,but it's going to take a lot more effort then Taylor.The IDEAL thing to do would be to work through both books simultaneously for a fantastic course in first year graduate analysis. And please don't torture yourself with Rudin's Real And Complex Analysis. It's sole purpose seems to be to see how much analysis can be crammed incomprehensibly into a single text. Folland is the same level and is much more accessible. That should get you started.Good luck!