Nonstandard Analysis for the Working Mathematician

• Corporate Author: SpringerLink (Online service)
• Other Authors: Loeb, Peter A. (Editor), Wolff, Manfred P. H. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2015.
• Edition: 2nd ed. 2015.
• Subjects: Mathematics.; Functional analysis.; Measure theory.; Operator theory.; Game theory.; Mathematical logic.; Number theory.; Functional Analysis.; Measure and Integration.; Operator Theory.; Game Theory, Economics, Social and Behav. Sciences.; Mathematical Logic and Foundations.; Number Theory.

Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is...

Table of Contents:

• Simple Nonstandard Analysis and Applications
• An Introduction to General Nonstandard Analysis
• Topology and Measure Theory
• Banach Spaces and Linear Operators
• General and End Compactifications
• Measure theory and integration
• Stochastic Analysis
• New Understanding of Stochastic Independence
• Nonstandard Analysis in Mathematical Economics
• Density Problems and Freiman's Inverse Problem
• Hypernatural numbers as ultrafilters.