Measures, Integrals and Martingales René L. Schilling is an English-language textbook that focuses on the core concepts of measure and integration and martingales. The book is suitable for students in higher education and professionals who are looking for a thorough introduction.
This textbook provides a clear and concise introduction to the theory of measure and integration, with extensive attention to martingales as an extension of the theory. Important topics such as Jacobi's transformation theorem, the Radon-Nikodym theorem, differentiation of measures, and Hardy-Littlewood maximal functions are discussed. In the second edition, new chapters have been added on, among other topics, Hausdorff measures, Fourier analysis, and vague convergence. All proofs are worked out in detail to facilitate deep understanding.
The book requires little prior knowledge and is therefore suitable for self-study or use in undergraduate courses. With more than 400 exercises and many illustrations, it aligns well with programs in probability, analysis, and applied mathematics.
This work is a valuable addition in the field of measure and integration and martingales and forms a logical follow-up to Schilling’s Counterexamples in Measure and Integration.