Extending isometrically invariant measures on \(R^ n\) -- a solution to Ciesielski's query (Q1374533)
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scientific article; zbMATH DE number 1095849
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extending isometrically invariant measures on \(R^ n\) -- a solution to Ciesielski's query |
scientific article; zbMATH DE number 1095849 |
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Extending isometrically invariant measures on \(R^ n\) -- a solution to Ciesielski's query (English)
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10 December 1997
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The author shows that it is always possible to extend an isometrically invariant measure on \(R^n\) in such a way that the corresponding measure algebra extends as well. This answers the question posed by \textit{K. Ciesielski} [Real Analysis Exchange 16, No.1, 374 (1991)]. The method the author uses is quite inventive, and no special set-theory axioms are employed [cf. \textit{A. Hulanicki}, Fundam. Math. 51, 111-115 (1962; Zbl 0113.04002)].
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invariant \(\sigma\)-finite measures
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isometries of \(R^ n\)
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extensions of measures
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0.92511654
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0.91874784
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0.88313246
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0.88169074
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0.88145906
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0.88042474
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0.87918335
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0.87557876
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