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Extending isometrically invariant measures on \(R^ n\) – a solution to Ciesielski’s query. (English) Zbl 0879.28024

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 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. A. Hulanicki, Fundam. Math. 51, 111-115 (1962; Zbl 0113.04002)].
Reviewer: P.Pták (Praha)

MSC:

28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
03E05 Other combinatorial set theory

Citations:

Zbl 0113.04002
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