| 书目名称 | Nonstandard Analysis | | 副标题 | Theory and Applicati | | 编辑 | Leif O. Arkeryd,Nigel J. Cutland,C. Ward Henson | | 视频video | | | 丛书名称 | Nato Science Series C: | | 图书封面 |  | | 描述 | 1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson‘s original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) inventi | | 出版日期 | Book 1997 | | 关键词 | Measure; Navier-Stokes equation; Probability theory; analysis; functional analysis; hydromechanics; fluid- | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-011-5544-1 | | isbn_softcover | 978-94-010-6335-7 | | isbn_ebook | 978-94-011-5544-1Series ISSN 1389-2185 | | issn_series | 1389-2185 | | copyright | Springer Science+Business Media Dordrecht 1997 |
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发表于 2025-3-21 17:59:59
