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On translation-bounded measures

Part of: Classical measure theory Stochastic processes

Published online by Cambridge University Press:  09 April 2009

A. P. Robertson  and
M. L. Thornett
A. P. Robertson
Affiliation:
Murdoch UniversityMurdoch, W.A. 6150, Australia
M. L. Thornett
Affiliation:
University of Western AustraliaNedlands, W.A. 6009, Australia
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Abstract

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It is shown that a positive measure μ on the Borel subsets of Rk is translation-bounded if and only if the Fourier transform of the indicator function of every bounded Borel subset of Rk belongs to L2(μ).

MSC classification

Secondary: 60G10: Stationary processes 28A33: Spaces of measures, convergence of measures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 1 , August 1984 , pp. 139 - 142
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Dunford, N. and Schwartz, J. T., Linear operators, part I: General theory (Interscience, New York, 1958).Google Scholar
[2]Robertson, A. P., ‘Unconditional convergence and the Vitali-Hahn-Saks theorem’, Colloque Anal. Function. [1971, Bordeaux] Bull. Soc. Math. France, Mémoire 31–32 (1972), 335–341.CrossRefGoogle Scholar
[3]Thornett, M. L., ‘A class of second-order stationary random measures’, Stochastic Processes Appl. 8 (1979), 323–334.CrossRefGoogle Scholar