Extensions of isometrically invariant measures on Euclidean spaces
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- by Piotr Zakrzewski PDF
- Proc. Amer. Math. Soc. 110 (1990), 325-331 Request permission
Abstract:
We consider countably additive, nonnegative, extended real-valued measures that vanish on singletons. Given a group $G$ of isometries of ${{\mathbf {R}}^n}$ and a $G$-invariant $\sigma$-finite measure on ${{\mathbf {R}}^n}$ we study the problem of determining whether it has a proper $G$-invariant extension. We prove that it does, provided that the set of all points with uncountable $G$-orbits is not of measure zero. We also characterize those groups $G$ for which every $G$-invariant $\sigma$-finite measure on ${{\mathbf {R}}^n}$ has a proper $G$-invariant extension.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 325-331
- MSC: Primary 28C10; Secondary 03E05
- DOI: https://doi.org/10.1090/S0002-9939-1990-1021216-3
- MathSciNet review: 1021216