Ebook: Basic analysis IV: measure theory and integration
Author: Peterson James Kent
- Tags: Integrals, MATHEMATICS / Applied, MATHEMATICS / Functional Analysis, Measure theory, Electronic books
- Year: 2021
- Publisher: CRC Press
- City: Boca Raton, FL
- Edition: First edition
- Language: English
- pdf
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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