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February, 1974 Weak Convergence of Certain Vectorvalued Measures
Paul Ressel
Ann. Probab. 2(1): 136-142 (February, 1974). DOI: 10.1214/aop/1176996758

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.

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Paul Ressel. "Weak Convergence of Certain Vectorvalued Measures." Ann. Probab. 2 (1) 136 - 142, February, 1974. https://doi.org/10.1214/aop/1176996758

Information

Published: February, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0291.28011
MathSciNet: MR360993
Digital Object Identifier: 10.1214/aop/1176996758

Subjects:
Primary: 28A45
Secondary: 60G10

Keywords: continuity-theorem , Fourier and Laplace transform , multiplicative measure , Orthogonal measure , weak convergence , Weakly stationary process

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 1 • February, 1974
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