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Lectures on the Hyperreals 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Robert Goldblatt 作者

Springer

译者

1998-10-01 出版日期

307 页数

USD 79.95 价格

Hardcover

Graduate Texts in Mathematics 丛书系列

9780387984643 图书编码

Lectures on the Hyperreals 在线电子书图书标签: 数学 Math 非标准分析

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Lectures on the Hyperreals 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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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.

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