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Results tagged with nonstandard-analysis
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user 26809
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.
9
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Hyperreal finitely-additive measure on [0,1) assigning $b-a$ to $[a,b)$ or $(a,b]$ and infin...
Is there a hyperreal-valued finitely additive measure on all the subsets of [0,1), or at least the Borel ones, that
assigns $b-a$ to $[a,b)$ and to $(a,b]$ for all $a\lt b,$ and
assigns an infinit …
- 2,555
4
votes
0
answers
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Self homomorphisms of hyperreals fixing the reals
What do we know about the circumstances (whether having to do with the axioms of set theory or the model itself) under which a field $F$ of hyperreals (=ultrapower of $\mathbb R$ with respect to a non …
- 2,555
3
votes
2
answers
294
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Hyperfinite set containing the reals, with specified upper bound on internal cardinality?
Is this true? For any hyperfinite $n$ that isn't finite, there is a hyperfinite set $A$ such that $\mathbb R \subset A$ and $|A|\le n$ (that's the crucial part, of course)? Intuitively it seems righ …
- 2,555
3
votes
1
answer
319
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A stronger version of supramenability?
A group $G$ is supramenable iff for all $\varnothing\ne A\subseteq G$ there is a finitely-additive left-$G$-invariant measure $\mu_A$ on $G$ with $\mu_A(A)=1$. I'm interested in a seemingly stronger …
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