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The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with a background in undergraduate mathematics. In its various forms, the manuscript was used by the second author in several graduate courses at the University of Illinois at Urbana-Champaign. The first chapter and parts of the rest of the book can be used in an advanced undergraduate course. Research mathematicians who want a quick introduction to nonstandard analysis will also find it useful. The main addition of this book to the contributions of previous textbooks on nonstan
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This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
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Mathematical logic --- Differential equations --- Nonstandard mathematical analysis --- Analyse mathématique non standard --- 517 --- Analysis --- Nonstandard mathematical analysis. --- 517 Analysis --- Analyse mathématique non standard --- Analyse non standard --- Equations differentielles --- Theorie asymptotique
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Nonstandard mathematical analysis --- Analyse mathématique non standard --- Nonstandard mathematical analysis. --- 517.13 --- Analysis, Nonstandard mathematical --- Mathematical analysis, Nonstandard --- Non-standard analysis --- Nonstandard analysis --- Model theory --- Theory of real numbers --- 517.13 Theory of real numbers --- Analyse mathématique non standard
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Provability, Computability and Reflection
Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- 517.1 --- 517.1 Introduction to analysis --- Introduction to analysis --- Nonstandard mathematical analysis --- Logic, symbolic and mathematical --- Analyse mathématique non standard --- Nonstandard mathematical analysis.
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