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Nonstandard Analysis

  • Martin Väth

Table of contents

  1. Front Matter
    Pages i-viii
  2. Martin Väth
    Pages 1-21
  3. Martin Väth
    Pages 23-57
  4. Martin Väth
    Pages 59-102
  5. Martin Väth
    Pages 103-124
  6. Martin Väth
    Pages 197-209
  7. Back Matter
    Pages 211-252

About this book

Introduction

Nonstandard analysis was originally developed by Robinson to rigorously justify infinitesimals like df and dx in expressions like df/dx in Leibniz' calculus or even to justify concepts like \delta-`functions'. However, the approach is much more general and was soon extended by Henson, Luxemburg and others to a useful tool especially in more advanced analysis, topology, and functional analysis. The book is an introduction with emphasis on those more advanced applications in analysis which are hardly accessible by other methods. Examples of such topics are a deeper analysis of certain functionals like Hahn-Banach limits or of finitely additive measures: From the viewpoint of classical analysis these are strange objects whose mere existence is even hard to prove. From the viewpoint of nonstandard analysis, these are rather 'explicit' objects.

Formally, nonstandard analysis is an application of model theory in analysis. However, the reader of the book is not expected to have any background in model theory; instead knowledge of calculus is required and, although the book is rather self-contained, background in more advanced analysis or (elementary) topology is useful.

Keywords

calculus differential equation functional analysis model theory nonstandard analysis

Authors and affiliations

  • Martin Väth
    • 1
  1. 1.Fachbereich Mathematik und Informatik (WE1)Freie Universität BerlinBerlinGermany

Bibliographic information

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