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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: 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.

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