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- DescriptionAn introduction to nstandard 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 nstandard analysis t 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 nstandard 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 nstandard 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.
- Author(s)Robert Goldblatt
- PublisherSpringer-Verlag New York Inc.
- Date of Publication03/10/2012
- Series TitleGraduate Texts in Mathematics
- Series Part/Volume Number188
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight480 g
- Width156 mm
- Height234 mm
- Spine16 mm
- Format DetailsTrade paperback (US)
- Edition StatementSoftcover reprint of the original 1st ed. 1998
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