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Isometrically invariant extensions of Lebesgue measure

Author: Krzysztof Ciesielski
Journal: Proc. Amer. Math. Soc. 110 (1990), 799-801
MSC: Primary 28C10
MathSciNet review: 1027089
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Abstract: The purpose of this note is to give a very short prove of the theorem thta every isometrically invariant measure extending Lebesgue measure on $ {{\mathbf{R}}^n}$ has a proper isometrically invariant extension, i.e., that there is no maximal isometrically invariant extension of Lebesgue measure on $ {{\mathbf{R}}^n}$.

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