
- 499 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
About this book
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
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Information
Table of contents
- Cover
- Half Title
- Title Page
- Copyright Page
- Dedication
- Table of Contents
- I Introductory Matter
- II Classical Riemann Integration
- III Riemann - Stieltjes Integration
- IV Abstract Measure Theory One
- V Constructing Measures
- VI Abstract Measure Theory Two
- VII Summing It All Up
- VIII References
- IX Detailed Index
- X Appendix: Undergraduate Analysis Background Check
- XI Appendix: Linear Analysis Background Check
- XII Appendix: Preliminary Examination Check