Nonstandard Analysis (SAP Excellence) by Martin Andreas Väth (PDF)

Description

This book introduces Robinson’s nonstandard analysis, an application of model theory in analysis. Unlike some texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but points to some applications in more advanced analysis. The contents proceed from a discussion of the preliminaries to Nonstandard Models; Nonstandard Real Analysis; Enlargements and Saturated Models; Functionals, Generalized Limits, and Additive Measures; and finally Nonstandard Topology and Functional Analysis. No background in model theory is required, although some familiarity with analysis, topology, or functional analysis is useful. This self-contained book can be understood after a basic calculus course.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This one is an excellent reference on constructions of nonstandard extensions and various properties related to such extensions. I would recommend this one as a second book on nonstandard analysis after Goldblatt’s excellent

⭐.

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