2007

The Strength of Nonstandard Analysis

Editors:

ISBN: 978-3-211-49904-7 (Print) 978-3-211-49905-4 (Online)

Table of contents (25 chapters)

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  1. Front Matter

    Pages i-xx

  2. Foundations

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-26

      The strength of nonstandard analysis

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      Book Chapter

      Pages 27-32

      The virtue of simplicity

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      Book Chapter

      Pages 33-46

      Analysis of various practices of referring in classical or non standard mathematics

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      Book Chapter

      Pages 47-63

      Stratified analysis?

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      Book Chapter

      Pages 64-75

      ERNA at work

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      Book Chapter

      Pages 76-91

      The Sousa Pinto approach to nonstandard generalised functions

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      Book Chapter

      Pages 92-116

      Neutrices in more dimensions

  3. Number theory

    1. Front Matter

      Pages 117-117

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      Book Chapter

      Pages 119-132

      Nonstandard methods for additive and combinatorial number theory. A survey

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      Book Chapter

      Pages 133-142

      Nonstandard methods and the Erdős-Turán conjecture

  4. Statistics, probability and measures

    1. Front Matter

      Pages 143-143

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      Book Chapter

      Pages 145-169

      Nonstandard likelihood ratio test in exponential families

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      Book Chapter

      Pages 170-176

      A finitary approach for the representation of the infinitesimal generator of a markovian semigroup

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      Book Chapter

      Pages 177-188

      On two recent applications of nonstandard analysis to the theory of financial markets

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      Book Chapter

      Pages 189-205

      Quantum Bernoulli experiments and quantum stochastic processes

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      Book Chapter

      Pages 206-216

      Applications of rich measure spaces formed from nonstandard models

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      Book Chapter

      Pages 217-226

      More on S-measures

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      Book Chapter

      Pages 227-237

      A Radon-Nikodým theorem for a vector-valued reference measure

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      Book Chapter

      Pages 238-249

      Differentiability of Loeb measures

  5. Differential systems and equations

    1. Front Matter

      Pages 251-251

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      Book Chapter

      Pages 253-270

      The power of Gâteaux differentiability

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      Book Chapter

      Pages 271-285

      Nonstandard Palais-Smale conditions

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      Book Chapter

      Pages 286-305

      Averaging for ordinary differential equations and functional differential equations

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