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A calculus proof of the Cramér-Wold theorem


Authors: Russell Lyons and Kevin Zumbrun
Journal: Proc. Amer. Math. Soc. 146 (2018), 1331-1334
MSC (2010): Primary 60E10; Secondary 44A12, 53C65
DOI: https://doi.org/10.1090/proc/13794
Published electronically: October 12, 2017
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Abstract: We present a short, elementary proof not involving Fourier transforms of the theorem of Cramér and Wold that a Borel probability measure is determined by its values on half-spaces.


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Additional Information

Russell Lyons
Affiliation: Department of Mathematics, 831 East 3rd Street, Indiana University, Bloomington, Indiana 47405-7106
Email: rdlyons@indiana.edu

Kevin Zumbrun
Affiliation: Department of Mathematics, 831 East 3rd Street, Indiana University, Bloomington, Indiana 47405-7106
Email: kzumbrun@indiana.edu

DOI: https://doi.org/10.1090/proc/13794
Keywords: Distributions of probability measures, Radon tranform, integral geometry
Received by editor(s): July 11, 2016
Received by editor(s) in revised form: April 22, 2017
Published electronically: October 12, 2017
Additional Notes: This research was partially supported by NSF grants DMS-1007244 and DMS-1400555
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2017 American Mathematical Society

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