Lectures on hyperreals. An introduction to nonstandard analysis.

Goldblatt, Robert:

ISBN 10: 038798464X / ISBN 13: 9780387984643

Edité par New York, Springer-Verlag, 2010

A propos de cet article

XIV, 289 p. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-05165 9780387984643 Sprache: Englisch Gewicht in Gramm: 550. N° de réf. du vendeur 2491413

Détails bibliographiques

Titre : Lectures on hyperreals. An introduction to ...

Éditeur : New York, Springer-Verlag

Date d'édition : 2010

Reliure : Hardcover

A propos de ce titre

Synopsis :

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.