Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60B15, 60E10

Retrieve articles in all journals with MSC: 60B15, 60E10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687648-4
PII: S 0002-9939(1983)0687648-4
Article copyright: © Copyright 1983 American Mathematical Society