Advances in Analysis, Probability and Mathematical Physics
Subtitle: Contributions of Nonstandard Analysis
By: edited by Sergio A. Albeverio, Wilhelm A. J. Luxemburg, Manfred P. H. Wolff
Contributors: Luxemburg, Wilhelm A. J.; Wolff, Manfred P. H.
Series: Mathematics and Its Applications -- 314; Mathematics and Its Applications -- 314
Publisher: Springer Netherlands
Published: 1995
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 251
ISBN-13: 9789048144815; 9789401584517
Subjects: Geometry; Mathematics; Global analysis (Mathematics); Statistics
Description: 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.
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