Berg, Imme

The Strength of Nonstandard Analysis

The Strength of Nonstandard Analysis


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ISBN: 9783211499054
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Table of contents

Part I. Foundations

1. The strength of nonstandard analysis
H. Jerome Keisler

2. The virtue of simplicity
Edward Nelson

3. Analysis of various practices of referring in classical or non standard mathematics
Yves Péraire

4. Stratified analysis?
Karel Hrbacek

5. ERNA at work
C. Impens, S. Sanders

6. The Sousa Pinto approach to nonstandard generalised functions
R. F. Hoskins

7. Neutrices in more dimensions
Imme Berg

Part II. Number theory

8. Nonstandard methods for additive and combinatorial number theory. A survey
Renling Jin

9. Nonstandard methods and the Erdos-Turán conjecture
Steven C. Leth

Part III. Statistics, probability and measures

10. Nonstandard likelihood ratio test in exponential families
Jacques Bosgiraud

11. A finitary approach for the representation of the infinitesimal generator of a markovian semigroup
Schérazade Benhabib

12. On two recent applications of nonstandard analysis to the theory of financial markets
Frederik S. Herzberg

13. Quantum Bernoulli experiments and quantum stochastic processes
Manfred Wolff

14. Applications of rich measure spaces formed from nonstandard models
Peter Loeb

15. More on S-measures
David A. Ross

16. A Radon-Nikodým theorem for a vector-valued reference measure
G. Beate Zimmer

17. Differentiability of Loeb measures
Eva Aigner

Part IV. Differential systems and equations

18. The power of Gâteaux differentiability
Vitor Neves

19. Nonstandard Palais-Smale conditions
Natália Martins, Vítor Neves

20. Averaging for ordinary differential equations and functional differential equations
Tewfik Sari

21. Path-space measure for stochastic differential equation with a coefficient of polynomial growth
Toru Nakamura

22. Optimal control for Navier-Stokes equations
Nigel J. Cutland, Katarzyna Grzesiak

23. Local-in-time existence of strong solutions of the n-dimensional Burgers equation via discretizations
João Paulo Teixeira

Part V. Infinitesimals and education

24. Calculus with infinitesimals
Keith D. Stroyan

25. Pre-University Analysis
Richard O’Donovan


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Keywords: MATHEMATICS / General MAT000000

Publication year
Natural Sciences

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