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Lectures on the Hyperreals : an Introduction to Nonstandard Analysis /

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This is an introduction to nonstandard analysis based on a course of lectures given several times by the author. It is suitable for use as a text at the beginning graduate or upper undergraduate level, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analys...

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Bibliographic Details
Main Author: Goldblatt, Robert
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York, 1998.
Series:Graduate texts in mathematics ; 188.
Subjects:
Mathematics.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • What are the Hyperreals?- Large Sets
  • Ultrapower Construction of the Hyperreals
  • The Transfer Principle
  • Hyperreals Great and Small
  • Convergence of Sequences and Series
  • Continuous Functions
  • Differentiation
  • The Riemann Integral
  • Topology of the Reals
  • Internal and External Sets
  • Internal Functions and Hyperfinite Sets
  • Universes and Frameworks
  • The Existence of Nonstandard Entities
  • Permanence, Comprehensiveness, Saturation
  • Loeb Measure
  • Ramsey Theory
  • Completion by Enlargement
  • Hyperfinite Approximation
  • Books on Nonstandard Analysis.