Measure and Integration: Concepts, Examples, and Applications

Measure and Integration: Examples, Concepts, and Applications instructs in core proofs, theorems, and approaches of real analysis, as illustrated via compelling exercises and carefully crafted, practical examples. From chapter one onward, students are asked to apply concepts to reinforce understanding and gain applied experience in real analysis. In particular, exercises challenge students to use key proofs of major real analysis theorems to encourage independent thinking and problem solving, and new areas of research powered by real analysis are introduced. Following early chapters on core concepts and approaches of real analysis, the authors apply real analysis across integration on product spaces, radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among other topics. Advanced exercises are also included at the end of each chapter, with exercise difficulty level noted for instructors, and solutions included in an appendix.