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Introduction to nonstandard analysis
Journal of Mathematical Physics, 1973Nonstandard analysis is a recent branch of mathematics in which usual notions about analysis and topology can be formulated in an attractive and condensed manner. The main feature of this theory is that it introduces the concept of infinitely large or small numbers and that it allows one to compute with them in exactly the same way as in ordinary ...
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Recent developments in problems with nonstandard growth and nonuniform ellipticity
Journal of Mathematical Analysis and Applications, 2021Giuseppe Mingione +1 more
exaly
1983
In diesem Kapitel wollen wir den Korper ℝ der reellen Zahlen zu einem Korper *ℝ erweitern, in dem es unendlich kleine und unendlich grose „Zahlen“ gibt. Insbesondere lassen sich in *ℝ die Leibnizschen Differentiale dx, dy exakt definieren und ein Zusammenhang des Differentialquotienten dy/dx mit der Ableitung f’(x) einer Funktion y = f(x) an der Stelle
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In diesem Kapitel wollen wir den Korper ℝ der reellen Zahlen zu einem Korper *ℝ erweitern, in dem es unendlich kleine und unendlich grose „Zahlen“ gibt. Insbesondere lassen sich in *ℝ die Leibnizschen Differentiale dx, dy exakt definieren und ein Zusammenhang des Differentialquotienten dy/dx mit der Ableitung f’(x) einer Funktion y = f(x) an der Stelle
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Foundations of Nonstandard Analysis
1997There are many introductions to nonstandard analysis, (some of which are listed in the References) so why write another one? All of the existing introductions have one or more of the following features: (A) heavy use of logical formalism right from the start; (B) early introduction of set theoretic apparatus in excess of what is needed for most ...
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