Lectures on the Hyperreals: An Introduction to Nonstandard Analysis

Goldblatt, Robert

ISBN 10: 038798464X / ISBN 13: 9780387984643

Edité par Springer, 1998

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Détails bibliographiques

Titre : Lectures on the Hyperreals: An Introduction ...

Éditeur : Springer

Date d'édition : 1998

Reliure : Couverture rigide

Etat : New

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Synopsis :

Book by Goldblatt Robert

Présentation de l'éditeur:

An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.