[PDF] Principles of Real Analysis, Third Edition

ISBN: 0120502577

Category: Tutorial

Posted on 2018-01-09, by luongquocchinh.


Author: Charalambos D. Aliprantis | Publisher: Academic Press | Category: Mathematics | Language: English | Page: 415 | ISBN: 0120502577 | ISBN13: 9780120502578 |

Description: This is the third edition of Principles of Real Analysis, first published in 1981. The aim of this edition is to accommodate the current needs for the traditional real analysis course that is usually taken by the senior undergraduate or by the first year graduate student in mathematics. This edition differs substantially from the second edition. Each chapter has been greatly improved by incorporating new material and by rearranging the old material. Moreover, a new chapter (Chapter 6) on Hilbert spaces and Fourier analysis has been added. The subject matter of the book focuses on measure theory and the Lebesgue integral as well as their applications to several functional analytic directions. As in the previous editions, the presentation of measure theory is built upon the notion of a semi ring in connection with the classical Caratheodory extension procedure. We believe that this natural approach can be easily understood by the student. An extra bonus of the presentation of measure theory via the semiring approach is the fact that the product of semirings is always a semi ring while the product of a-algebras is a semiring but not a a-algebra. This simple but important fact demonstrates that the

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