Open Access
April, 1973 Subgroups of Paths and Reproducing Kernels
Raoul Le Page
Ann. Probab. 1(2): 345-347 (April, 1973). DOI: 10.1214/aop/1176996990


The following generalizations of certain theorems due to G. Kallianpur and to Jamison and Orey are proved for an arbitrary Gaussian measure $P$ on a space of real functions: if the reproducing kernel Hilbert space $H$ is infinite dimensional then $P(H) = 0$; if a subgroup $G$ of the space of real functions (under addition) is measurable with respect to the $P$-completion of the Borel product sigma-algebra, then $P(G) = 0$ or $P(G) = 1$ and in the latter case $H \subset G$.


Download Citation

Raoul Le Page. "Subgroups of Paths and Reproducing Kernels." Ann. Probab. 1 (2) 345 - 347, April, 1973.


Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0353.60037
MathSciNet: MR350835
Digital Object Identifier: 10.1214/aop/1176996990

Primary: 60G15
Secondary: 60F20

Keywords: Gaussian measure , reproducing kernel , subgroup

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 2 • April, 1973
Back to Top