A Sharp Form of the Cramér–Wold Theorem

Juan Antonio Cuesta-Albertos (), Ricardo Fraiman () and Thomas Ransford ()
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Juan Antonio Cuesta-Albertos: Universidad de Cantabria
Ricardo Fraiman: Universidad de San Andrés
Thomas Ransford: Université Laval

Journal of Theoretical Probability, 2007, vol. 20, issue 2, 201-209

Abstract: Abstract The Cramér–Wold theorem states that a Borel probability measure P on ℝ d is uniquely determined by its one-dimensional projections. We prove a sharp form of this result, addressing the problem of how large a subset of these projections is really needed to determine P. We also consider extensions of our results to measures on a separable Hilbert space.

Keywords: Probability measures; Projections; Cramér-Wold theorem; Hilbert spaces (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10959-007-0060-7

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