Basic analysis IV : measure theory and integration
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書誌事項
Basic analysis IV : measure theory and integration
Chapman & Hall/CRC, 2020
- hbk.
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内容説明・目次
内容説明
Basic Analysis IV: Measure Theory and Integration introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides.
Features
* Can be used as a traditional textbook as well as for self-study
* Suitable for advanced students in mathematics and associated disciplines
* Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
目次
1.Introduction. 2. An Overview Of Riemann Integration. 3. Functions Of Bounded Variation. 4.The Theory Of Riemann Integration. 5. Further Riemann Integration Results. 6. The Riemann-Stieltjes Integral. 7. Further Riemann - Stieljes Results. 8. Measurable Functions and Spaces. 9. Measure And Integration. 10. The Lp Spaces. 11. Constructing Measures. 12. Lebesgue Measure. 13. Cantor Set Experiments. 14. Lebesgue Stieljes Measure. 15. Modes Of Convergence. 16. Decomposition Of Measures. 17. Connections To Riemann Integration. 18. Fubini Type Results. 19. Differentiation. 20. Summing It All Up. References. Index. Appendix A. Appendix B. Appendix C. Appendix D.
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