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.

引用

页码：201 / 209

页数：9

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