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Nonstandard Methods of Analysis 🔍
Anatoly G. Kusraev, Semen S. Kutateladze (auth.) Springer Netherlands : Imprint : Springer, Mathematics and Its Applications 291, 1, 1994
英语 [en] · PDF · 10.5MB · 1994 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
__Nonstandard Methods of Analysis__ is concerned with the main trends in this field; infinitesimal analysis and Boolean-valued analysis. The methods that have been developed in the last twenty-five years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Boolean-valued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years. For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work.
备用文件名
lgrsnf/A:\compressed\10.1007%2F978-94-011-1136-2.pdf
备用文件名
nexusstc/Nonstandard Methods of Analysis/5b84f65fb08dbdbe35a8e2021f468c9c.pdf
备用文件名
scihub/10.1007/978-94-011-1136-2.pdf
备用文件名
zlib/Mathematics/Anatoly G. Kusraev, Semen S. Kutateladze (auth.)/Nonstandard Methods of Analysis_2129230.pdf
备选作者
A. G. Kusraev, Semën Samsonovich Kutateladze
备用出版商
Springer Science+Business Media, B.V
备用出版商
Springer Science + Business Media BV
备用出版商
Kluwer Academic Publishers
备用版本
Mathematics and its applications (Kluwer Academic Publishers), v. 291, Dordrecht ; Boston, ©1994
备用版本
Springer Nature, Dordrecht, 2012
备用版本
Netherlands, Netherlands
元数据中的注释
sm21682571
元数据中的注释
{"edition":"1","isbns":["940104497X","9401111367","9789401044974","9789401111362"],"last_page":439,"publisher":"Springer Netherlands","series":"Mathematics and Its Applications 291"}
备用描述
This volume is devoted to nonstandard methods of analysis based on applying nonstandard models of set theory. The present monograph is concerned with the main trends in this field, infinitesimal analysis and Boolean-valued analysis. Here, the methods that have been developed in the last twenty-five years are explained in detail, and are collected in bookform for the first time.
Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Boolean-valued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that were developed in recent years.
备用描述
Front Matter....Pages i-viii
Front Matter....Pages 1-2
Excursus into the History of Mathematical Analysis....Pages 3-12
Naive Fundamentals of Infinitesimal Methods....Pages 13-40
Set-Theoretic Formalisms of Nonstandard Analysis....Pages 41-80
Monads in General Topology....Pages 81-111
Infinitesimals and Subdifferentials....Pages 112-168
Front Matter....Pages 169-171
Universes of Sets....Pages 171-213
Boolean-Valued Universes....Pages 214-262
Functors of Boolean-Valued Analysis....Pages 263-323
Boolean-Valued Analysis of Algebraic Systems....Pages 324-376
Boolean Representations in Functional Analysis....Pages 377-403
Back Matter....Pages 404-439
备用描述
Mathematics and Its Applications
Erscheinungsdatum: 20.10.2012
开源日期
2013-08-01
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