Measures, Integrals and Martingales

Review of previous edition: ‘… thorough introduction to a wide variety of first-year graduate-level topics in analysis … accessible to anyone with a strong undergraduate background in calculus, linear algebra and real analysis.’ Zentralblatt MATHReview of previous edition: ‘The author truly covers a wide range of topics … Proofs are written in a very organized and detailed manner … I believe this to be a great book for self-study as well as for course use. The book is ideal for future probabilists as well as statisticians, and can serve as a good introduction for mathematicians interested in measure theory.’ Ita Cirovic Donev, MAA ReviewsReview of previous edition: ‘… succeeds in handling the technicalities of measure theory, which is traditionally regarded as dry and inaccessible to students (and, I think, the most difficult material that I have taught at undergraduate level) with a light touch. The book is eminently suitable for a course (or two) for good final-year or first-year post-graduate students and has the potential to revitalize the way that measure theory is taught.’ N. H. Bingham, Journal of the Royal Statistical SocietyReview of previous edition: ‘This book will remain a good reference on the subject for years to come.’ Peter Eichelsbacher, Mathematical ReviewsReview of previous edition: ‘… this well-written and carefully structured book is an excellent choice for an undergraduate course on measure and integration theory. Most good books on measure and integration are graduate books and, therefore, are not optimal for undergraduate courses … This book is aimed at both (future) analysts and (future) probabilists, and is therefore suitable for students from both these groups.’ Filip Lindskog, Journal of the American Statistical Association‘This book is an admirable counterpart, both to the first author’s well-known text Measures, Integrals and Martingales (CUP, 2005⁄2017), and to the books on counter-examples in analysis (Gelbaum and Olmsted), topology (Steen and Seebach) and probability (Stoyanov). To paraphrase, the authors’ preface: in a good theory, it is valuable and instructive to probe the limits of what can be said by investigating what cannot be said. The task is thus well-conceived, and the execution is up to the standards one would expect from the books of the first author and of their papers. I recommend it warmly.’ Professor N. H. Bingham, Imperial College London

René L. Schilling is a Professor of Mathematics at Technische Universität, Dresden. His main research area is stochastic analysis and stochastic processes.