On Poincaré's remark and a kind of nonstandard measure defined on \(^*(R^n)\) (Q2739137)
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scientific article; zbMATH DE number 1643510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Poincaré's remark and a kind of nonstandard measure defined on \(^*(R^n)\) |
scientific article; zbMATH DE number 1643510 |
Statements
10 March 2002
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hyperfinite set
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Lebesgue outer hyperstandard measure
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Cantor's continuum
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On Poincaré's remark and a kind of nonstandard measure defined on \(^*(R^n)\) (English)
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From the fact that in saturated models of \(\mathbb R\), the real number system, \(\mathbb R\) can be embedded externally as a subset of a hyperfinite set of the model, one may view \(\mathbb R\) in the external world as part of a discrete set. The authors deduce from this point of view that the Lebesgue outer hyperstandard measure of \(\mathbb R\) is equal to zero. It is then argued that this result, nevertheless, in a sense is consistent with Poincaré's views concerning the nature of Cantor's continuum of real numbers.
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0.7296544909477234
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