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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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