Nonstandard Analysis and Its Applications

Nonstandard Analysis and Its Applications

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This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.
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Table of contents

Preface; Contributors; 1. An invitation to non standard analysis Tom Lindstrom; 2. Infinitesimal in probability theory H. Jerome Keisler; 3. Infinitesimals in functional analysis C. Ward Henson; 4. Applications of non standard analysis in mathematical physics Sergio Albervio; 5. A lattice formulation of real and vector valued integrals Peter A. Loeb; 6. An application of non standard methods to computational group theory B. Benninghofen and M.M. Richter; 7. Syntactical methods in infinitesimal analysis Francine Deiner and Keith D. Stroyan; 8. Some asymptotic results in ordinary differential equations Francine and Marc Diener; 9. Superinfinitesimals and inductive limits Keith D. Stroyan; 10. The non-linear boltzmann equation far from equilibrium Leif Arkeryd; Index.
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