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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
DOI: https://doi.org/10.1090/S0002-9939-1990-1027089-7
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}$.


References [Enhancements On Off] (What's this?)

  • [Ci1] K.Ciesielski, How good is Lebesgue measure?, Math. Intelligencer 11 (1989), 54-58. MR 994965 (90a:28001)
  • [Ci2] -, Algebraically invariant extensions of $ \sigma $-finite measures on Euclidean space, Trans. Amer. Math. Soc. 315 (1989).
  • [CP] K. Ciesielski and A. Pelc, Extensions of invariant measures on Eucledean spaces, Fund. Math. 125 (1985), 1-10. MR 813984 (87c:28017)
  • [Ha] A. B. Harazisvili, On Sierpinski's problem concerning strict extendibility of an invariant measure, Soviet Math. Dokl. 81 (1977), 71-74.
  • [Hu] A. Hulanicki, Invariant extensions of the Lebesgue measure, Fund. Math. 51 (1962), 111-115. MR 0142709 (26:278)
  • [La] S. Lang, Algebra, Addison-Wesley, 1984. MR 0197234 (33:5416)
  • [Pk] S. S. Pkhakadze, $ K$ teorii lebegovskoi miery, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR, vol. 25, 1958. (Russian)
  • [Ru] W. Rudin, Real and complex analysis, McGraw-Hill, 1987. MR 924157 (88k:00002)
  • [Sz] E. Szpilrajn, Sur l'extension de la mesure lebesguienne, Fund. Math. 25 (1935), 551-558. (French)

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DOI: https://doi.org/10.1090/S0002-9939-1990-1027089-7
Article copyright: © Copyright 1990 American Mathematical Society

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