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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1027089-7
PII: S 0002-9939(1990)1027089-7
Article copyright: © Copyright 1990 American Mathematical Society