A sharp form of the Cramer-Wold theorem

被引：47
|
作者：
Cuesta-Albertos, Juan Antonio [1 ]
Fraiman, Ricardo
Ransford, Thomas
机构：
[1] Univ Cantabria, Dept Matemat Estad & Computac, E-39005 Santander, Spain
[2] Univ San Andres, Dept Matemat & Ciencias, Buenos Aires, DF, Argentina
[3] Univ Laval, Dept Math & Stat, Ste Foy, PQ G1K 7P4, Canada
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2007年 / 20卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
probability measures; projections; Cramer-Wold theorem; Hilbert spaces;
D O I：
10.1007/s10959-007-0060-7
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
The Cramer-Wold theorem states that a Borel probability measure P on R-d supercript stop 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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页码：201 / 209
页数：9
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