An Introduction to Nonstandard Real Analysis

✍ Scribed by Albert E. Hurd; Peter A. Loeb

• Publisher: Academic Press
• Year: 2014
• Tongue: English
• Leaves: 238
• Series: Pure and Applied Mathematics 118
• Category: Library

✦ Synopsis

The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with a background in undergraduate mathematics. In its various forms, the manuscript was used by the second author in several graduate courses at the University of Illinois at Urbana-Champaign. The first chapter and parts of the rest of the book can be used in an advanced undergraduate course. Research mathematicians who want a quick introduction to nonstandard analysis will also find it useful. The main addition of this book to the contributions of previous textbooks on nonstandard analysis (12,37,42,46) is the first chapter, which eases the reader into the subject with an elementary model suitable for the calculus, and the fourth chapter on measure theory in nonstandard models.

✦ Table of Contents

Content:
Edited by
Page iii

Copyright Page
Page iv

Preface
Pages ix-xii

Chapter I Infinitesimals and The Calculus
Pages 1-69

Chapter II Nonstandard Analysis on Superstructures
Pages 70-108

Chapter III Nonstandard Theory of Topological Spaces
Pages 109-163

Chapter IV Nonstandard Integration Theory
Pages 164-218

Appendix Ultrafilters
Pages 219-221

References
Pages 222-224

List of Symbols
Pages 225-226

Index
Pages 227-232