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Advances in Analysis, Probability and Mathematical Physics: Contributions of Nonstandard Analysis

Albeverio, Sergio A. and Luxemburg, Wilhelm A. J. and Wolff, Manfred P. H. (1995) Advances in Analysis, Probability and Mathematical Physics: Contributions of Nonstandard Analysis. Mathematics and Its Applications. No.314. Springer , Dordrecht. ISBN 978-90-481-4481-5. https://resolver.caltech.edu/CaltechAUTHORS:20181012-074421607

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Abstract

In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he called 'Nonstandard analysis'. 'Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier. During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research. Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics. This volume can be used as a complementary text to courses in nonstandard analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics.


Item Type:Book
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-94-015-8451-7DOIBook
Additional Information:© 1995 Springer Science+Business Media B.V.
Subject Keywords:Probability theory; Variance; calculus; differential equation; mathematical physics
Series Name:Mathematics and Its Applications
Issue or Number:314
Record Number:CaltechAUTHORS:20181012-074421607
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181012-074421607
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90259
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Oct 2018 20:28
Last Modified:03 Oct 2019 20:23

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