Nonstandard Methods of Analysis - A. G. Kusraev

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Résumé :
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.

Sommaire:
I. Infinitesimal Analysis.- 1. Excursus into the History of Mathematical Analysis.- 2. Naive Fundamentals of Infinitesimal Methods.- 3 Set-Theoretic Formalisms of Nonstandard Analysis.- 4. Monads in General Topology.- 5. Infinitesimals and Subdifferentials.- 2. Boolean-Valued Analysis.- 1. Universes of Sets.- 2. Boolean-Valued Universes.- 3. Functors of Boolean-Valued Analysis.- 4. Boolean-Valued Analysis of Algebraic Systems.- 5. Boolean Representations in Functional Analysis.- References.