Dewey Class 
515 
Title 
Advances in Analysis, Probability and Mathematical Physics ([EBook] :) : Contributions of Nonstandard Analysis / / edited by Sergio A. Albeverio, Wilhelm A. J. Luxemburg, Manfred P. H. Wolff. 
Added Personal Name 
Albeverio, Sergio A. editor. 
Luxemburg, Wilhelm A. J. editor. 
Wolff, Manfred P. H. editor. 
Other name(s) 
SpringerLink (Online service) 
Publication 
Dordrecht : : Springer Netherlands : : Imprint: Springer, , 1995. 
Physical Details 
X, 252 p. : online resource. 
Series 
Mathematics and its applications ; 314 
ISBN 
9789401584517 
Summary Note 
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 firstorder 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.: 
Contents note 
Table of Content  I: Analysis  Singular traces and nonstandard analysis  NavierStokes equations  Hyperfinite approximations of commutative topological groups  A note on the myope topology  Nonlinear theories of generalized functions  A nonstandard approach to the Pettis integral  A counterexample to the spectral mapping theorem revisited from a nonstandard point of view  Nonstandard polynominals in several variables  An existence result for a class of partial differential equations with smooth coefficients  On the generation of topology by external equivalence relations  Nonstandard hulls of LebesgueBochner spaces  II: Probability Theory  A nonstandard approach to diffusions on manifolds and nonstandard heat kernels  A nonstandard approach to the Malliavin Calculus  Ergodic transformations in AST  Nonstandard characterization for a general invariance principle  Andersonsâ€™s Brownian motion and the infinite dimensional OrnsteinUhlenbeck process  Two applications of NSA in the theory of stochastic dynamical systems  Nonstandard methods and the space of experiments  III: Mathematical Physics  Infinite range forces and strong L1asymptotics for the spacehomogeneous Boltzmann equation  A nonstandard analysis approach to the theory of quantum meanfield systems. 
System details note 
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9789401584517 
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