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Full Description
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.
Contents
1. Abstract Integration
2. Measures
3. Integration on Product Spaces
4. The Lebesgue-Radon-Nikodym Theorem
5. Radon Functionals on Locally Compact Hausdorff Spaces
6. Differentiation
7. Functions of Bounded Variation and Lebesgue-Stieltjes Measures
8. Convolutions
9. Probability
10. Differential Equations with measure coefficients
11. Appendices
