Lectures on the Hyperreals An Introduction to Nonstandard Analysis
There are good reasons to believe that nonstandard analysis, in some ver sion or other, will be the analysis of the future. KURT GODEL This book is a compilation and development of lecture notes written for a course on nonstandard analysis that I have now taught several times. Students taking the c...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I Foundations
- 1 What Are the Hyperreals?
- 2 Large Sets
- 3 Ultrapower Construction of the Hyperreals
- 4 The Transfer Principle
- 5 Hyperreals Great and Small
- II Basic Analysis
- 6 Convergence of Sequences and Series
- 7 Continuous Functions
- 8 Differentiation
- 9 The Riemann Integral
- 10 Topology of the Reals
- III Internal and External Entities
- 11 Internal and External Sets
- 12 Internal Functions and Hyperfinite Sets
- IV Nonstandard Frameworks
- 13 Universes and Frameworks
- 14 The Existence of Nonstandard Entities
- 15 Permanence, Comprehensiveness, Saturation
- V Applications
- 16 Loeb Measure
- 17 Ramsey Theory
- 18 Completion by Enlargement
- 19 Hyperfinite Approximation
- 20 Books on Nonstandard Analysis