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Results tagged with nonstandard-analysis
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user 7139
Nonstandard analysis is a way of doing calculus and analysis with infinitesimals. The historical approach of Leibniz, Euler, and others to infinitesimal calculus was gradually replaced by epsilon, delta techniques in the context of a real continuum, in the 19th century. It was not until the 1960s that Abraham Robinson developed a theory of a hyperreal continuum that allows for a development of analysis procedurally akin to that of its founders.
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Ergodic Theorem and Nonstandard Analysis
Here is a quote from Lectures on Ergodic Theory by Halmos:
I cannot resist the temptation of
concluding these comments with an
alternative "proof" of the ergodic
theorem. If $f$ is a complex …
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