2.1.1 The Riemann Integral as a Limit . . . 2.1.2 TheFundamentalTheoremofCalculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 The Cauchy Fundamental Theorem of Calculus . 2.2 HandlingJumps .
Author: James K. Peterson
Publisher: CRC Press
ISBN: 9781351679244
Category: Mathematics
Page: 500
View: 162
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