Basic analysis IV : measure theory and integration / James K. Peterson.
By: Peterson, James K. (James Kent) [author.].
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BookPublisher: Boca Raton, FL : CRC Press, 2021Copyright date: ©2020Edition: First edition.Description: 1 online resource (xi, 488 pages) : illustrations.Content type: text Media type: computer Carrier type: online resourceISBN: 9781315166186; 1315166186; 9781351679244; 1351679244; 9781351679237; 1351679236; 9781351679220; 1351679228.Subject(s): Measure theory | Integrals | MATHEMATICS / Functional Analysis | MATHEMATICS / AppliedDDC classification: 515.42 Online resources: Taylor & Francis | OCLC metadata license agreement Summary: 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
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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