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


A theorem of Cramér and Wold revisited

Author: Alladi Sitaram
Journal: Proc. Amer. Math. Soc. 87 (1983), 714-716
MSC: Primary 60B15; Secondary 60E10
MathSciNet review: 687648
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ H = \{ (x,y);x > 0\} \subseteq {{\mathbf{R}}^2}$ and let $ E$ be a Borel subset of $ H$ of positive Lebesgue measure. We prove that if $ \mu $ and $ \upsilon $ are two probability measures on $ {{\mathbf{R}}^2}$ such that $ \mu (\sigma (E)) = \upsilon (\sigma (E))$ for all rigid motions $ \sigma $ of $ {{\mathbf{R}}^2}$, then $ \mu = \upsilon $ This generalizes a well-known theorem of Cramér and Wold.

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

  • [1] S. C. Bagchi and A. Sitaram, Determining sets for measures on 𝑅ⁿ, Illinois J. Math. 26 (1982), no. 3, 419–422. MR 658452 (83h:28020)
  • [2] W. F. Donoghue, Jr., Distributions and Fourier transforms, Academic Press, New York, 1969.
  • [3] William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154 (35 #1048)
  • [4] A. Hertle, Zur Radon-Transformation von Funktionen und Massen, Thesis, Erlangen, 1979.
  • [5] Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. McGraw-Hill Series in Higher Mathematics. MR 0365062 (51 #1315)

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PII: S 0002-9939(1983)0687648-4
Article copyright: © Copyright 1983 American Mathematical Society

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