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Results tagged with nonstandard-analysis
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user 935
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.
3
votes
Non Separability of the the Loeb Space
The background is, I suspect, the recent papers of Elek and Szegedy, in which the nonseparability of this space place a large (and confounding) role.
I strongly prefer the language of nonstandard ana …
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7
votes
nonstandard analysis book recommendation
I loved Goldblatt's book, "Lectures on the Hyperreals".
For a more sophisticated treatment, don't overlook "Nonstandard Analysis: Theory and Applications", edited by Henson (first chapter available t …
18
votes
How helpful is non-standard analysis?
Freiman conjectured a classification of finite sets $A$ of integers that have
$$\lvert A+A\rvert = 3\lvert A\rvert-3+b$$
for some $0\leq b \leq \lvert A\rvert/3-2$. Renling Jin recently resolved this …
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5
votes
A remark of Connes on non-standard analysis
I don't think this answer is fundamentally different from Joel's, but perhaps the differing exposition may help.
Every irrational real number in $[0,1]$ has a unique binary expansion, and so every ir …
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16
votes
Nonstandard analysis in probability theory
True probabilists have a rather unique way of thinking. It is, if you will allow word-creation, hyper-analytic. This thought pattern seems (anecdotally!) to not be too compatible with algebraic or log …
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