Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] Krzysztof Ciesielski, How good is Lebesgue measure?, Math. Intelligencer 11 (1989), no. 2, 54–58. MR 994965, 10.1007/BF03023824
  • [Ci2] -, Algebraically invariant extensions of $ \sigma $-finite measures on Euclidean space, Trans. Amer. Math. Soc. 315 (1989).
  • [CP] Krzysztof Ciesielski and Andrzej Pelc, Extensions of invariant measures on Euclidean spaces, Fund. Math. 125 (1985), no. 1, 1–10. MR 813984
  • [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 (1962/1963), 111–115. MR 0142709
  • [La] Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0197234
  • [Pk] S. S. Pkhakadze, $ K$ teorii lebegovskoi miery, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR, vol. 25, 1958. (Russian)
  • [Ru] Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987. MR 924157
  • [Sz] E. Szpilrajn, Sur l'extension de la mesure lebesguienne, Fund. Math. 25 (1935), 551-558. (French)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28C10

Retrieve articles in all journals with MSC: 28C10

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society