About this book
Nonstandard analysis was originally developed by Robinson to rigorously justify infinitesimals like df and dx in expressions like df/dx in Leibniz' calculus or even to justify concepts like \delta-`functions'. However, the approach is much more general and was soon extended by Henson, Luxemburg and others to a useful tool especially in more advanced analysis, topology, and functional analysis. The book is an introduction with emphasis on those more advanced applications in analysis which are hardly accessible by other methods. Examples of such topics are a deeper analysis of certain functionals like Hahn-Banach limits or of finitely additive measures: From the viewpoint of classical analysis these are strange objects whose mere existence is even hard to prove. From the viewpoint of nonstandard analysis, these are rather 'explicit' objects.
Formally, nonstandard analysis is an application of model theory in analysis. However, the reader of the book is not expected to have any background in model theory; instead knowledge of calculus is required and, although the book is rather self-contained, background in more advanced analysis or (elementary) topology is useful.
- Book Title Nonstandard Analysis
- DOI https://doi.org/10.1007/978-3-7643-7774-8
- Copyright Information Birkhäuser Basel 2007
- Publisher Name Birkhäuser, Basel
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-3-7643-7773-1
- eBook ISBN 978-3-7643-7774-8
- Edition Number 1
- Number of Pages VIII, 252
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
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