Nonstandard Analysis for the Working Mathematician / edited by Peter A. Loeb, Manfred P.H. Wolff
| データ種別 | 電子書籍 |
|---|---|
| 版 | 1st ed. 2000. |
| 出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
| 出版年 | 2000 |
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| 書誌ID | OB01026777 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | I An Introduction to Nonstandard Analysis by Peter A. Loeb -- 1 A Simple Introduction to Nonstandard Analysis -- 2 An Introduction to General Nonstandard Analysis -- 3 Topology and Measure Theory -- II Functional Analysis by Manfred P. H. Wolff -- 4 Functional Analysis -- III Measure and Probability Theory and Applications by Horst Osswald and Yeneng Sun -- 5 Measure Theory and Integration -- 6 Probability Theory -- 7 Conventional Operations on Nonstandard Constructions -- IV Economics and Nonstandard Analysis by Yeneng Sun -- 8 Nonstandard Analysis in Mathematical Economics. License restrictions may limit access Summary: This book is addressed to mathematicians working in analysis and its applications. The aim is to provide an understandable introduction to the basic theory of nonstan dard analysis in Part I, and then to illuminate some of its most striking applications. Much of the book, in particular Part I, can be used in a graduate course; problems are posed in all chapters. After Part I, each chapter takes up a different field for the application of nonstandard analysis, beginning with a gentle introduction that even non-experts can read with profit. The remainder of each chapter is then addressed to experts, showing how to use nonstandard analysis in the search for solutions of open problems and how to obtain rich new structures that produce deep insight into the field under consideration. The applications discussed here are in functional analysis including operator theory, probability theory including stochastic processes, and economics including game theory and financial mathematics. In all of these areas, the intuitive notion of an infinitely small or infinitely large quantity plays an essential and helpful role in the creative process. For example, Brownian motion is often thought of as a random walk with infinitesimal increments; the spectrum of a selfadjoint operator is viewed as the set of "almost eigenvalues"; an ideal economy consists of an infinite number of agents each having an infinitesimal influence on the economy. Already at the level of calculus, one often views the integral as an infinitely large sum of infinitesimal quantities |
| 著者標目 | Loeb, Peter A Wolff, Manfred P.H SpringerLink (Online service) |
| 統一書名標目 | Mathematics and Its Applications ; |
| 件 名 | LCSH:Functions of real variables LCSH:Probabilities LCSH:Mathematical logic FREE:Real Functions FREE:Probability Theory FREE:Mathematical Logic and Foundations |
| 分 類 | LCC:QA331.5 DC23:515.8 |
| 巻冊次 | ISBN:9789401141680 RefWorks出力（各巻） print ; ISBN:9780792363415 RefWorks出力（各巻） print ; ISBN:9780792363408 RefWorks出力（各巻） print ; ISBN:9789401141697 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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