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A Sharp Form of the Cramér–Wold Theorem

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Abstract

The Cramér–Wold theorem states that a Borel probability measure P on ℝd 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.

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Authors and Affiliations

  1. Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain

    Juan Antonio Cuesta-Albertos

  2. Departamento de Matemática y Ciencias, Universidad de San Andrés, Buenos Aires, Argentina

    Ricardo Fraiman

  3. Département de mathématiques et de statistique, Université Laval, Quebec, QC, Canada, G1K 7P4

    Thomas Ransford

Authors
  1. Juan Antonio Cuesta-Albertos
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  2. Ricardo Fraiman
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  3. Thomas Ransford
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Corresponding author

Correspondence to Juan Antonio Cuesta-Albertos.

Additional information

First author partially supported by the Spanish Ministerio de Ciencia y Tecnología, grant BFM2002-04430-C02-02.

Second author partially supported by Instituto de Cooperación Iberoamericana, Programa de Cooperación Interuniversitaria AL-E 2003.

Third author partially supported by grants from NSERC and the Canada research chairs program.

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Cuesta-Albertos, J.A., Fraiman, R. & Ransford, T. A Sharp Form of the Cramér–Wold Theorem. J Theor Probab 20, 201–209 (2007). https://doi.org/10.1007/s10959-007-0060-7

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  • DOI: https://doi.org/10.1007/s10959-007-0060-7

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