A Course in Real Analysis

Rating:
Summary: One of the better books on real analysis
Review: I have several books in real analysis including those by rudin, kolmogorov, reisz, etc. Of all the book I have on real analysis, this is by far the most lucid. It is thicker than all of them but only because the authors (McDonald and Weiss) spend time in explaining and motiviating the material. I have learned more in a shorter amount of time from this book than any other advanced math book I own (and I own at least 50 on everything from topology to stochastic processes to algebra). The proofs are clear and the steps are explained in layman's terms (at the level of something like Scientific American's typical readership). The material covers the Lebesgue theory of integration, abstract measure theory, mesure theoretic probability, hilbert spaces, etc. My goal is to learn stochastic calculus beyond the mere manipulation of Ito's lemma and I must say this book, more than any other, is getting me to that level of mathematical maturity quickly. Now I feel pretty confident I can understand that proof in HJM (for you finance buffs out there) involving the stochastic version of Fubini's theorem that always bugged me!

Rating:
Summary: One of the better books on real analysis
Review: I have several books in real analysis including those by rudin, kolmogorov, reisz, etc. Of all the book I have on real analysis, this is by far the most lucid. It is thicker than all of them but only because the authors (McDonald and Weiss) spend time in explaining and motiviating the material. I have learned more in a shorter amount of time from this book than any other advanced math book I own (and I own at least 50 on everything from topology to stochastic processes to algebra). The proofs are clear and the steps are explained in layman's terms (at the level of something like Scientific American's typical readership). The material covers the Lebesgue theory of integration, abstract measure theory, mesure theoretic probability, hilbert spaces, etc. My goal is to learn stochastic calculus beyond the mere manipulation of Ito's lemma and I must say this book, more than any other, is getting me to that level of mathematical maturity quickly. Now I feel pretty confident I can understand that proof in HJM (for you finance buffs out there) involving the stochastic version of Fubini's theorem that always bugged me!