The Annals of Probability

Weak Convergence of Certain Vectorvalued Measures

Paul Ressel

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Abstract

There are two kinds of vectorvalued measures which are involved in the theory of weakly stationary processes: orthogonal (Hilbert space valued) and multiplicative (projection-valued) measures. For both classes we show that weak convergence is equivalent with the convergence of integrals over bounded continuous functions. Moreover we prove continuity theorems for the Fourier transformation as well as for the Laplace transformation of such measures.

Article information

Source
Ann. Probab., Volume 2, Number 1 (1974), 136-142.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996758

Digital Object Identifier
doi:10.1214/aop/1176996758

Mathematical Reviews number (MathSciNet)
MR360993

Zentralblatt MATH identifier
0291.28011

JSTOR
links.jstor.org

Subjects
Primary: 28A45
Secondary: 60G10: Stationary processes

Keywords
Orthogonal measure multiplicative measure weak convergence continuity-theorem Fourier and Laplace transform weakly stationary process

Citation

Ressel, Paul. Weak Convergence of Certain Vectorvalued Measures. Ann. Probab. 2 (1974), no. 1, 136--142. doi:10.1214/aop/1176996758. https://projecteuclid.org/euclid.aop/1176996758


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