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Lp-convergence of a certain class of product martingales

Published online by Cambridge University Press:  20 January 2009

Stamatis Koumandos
Stamatis Koumandos
Affiliation:
Department of Pure Mathematics, The University of Adelaide, G.P.O. Box 498, Adelaide, 5001, South Australiae-mail address: [email protected]
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Abstract

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We establish the Kakutani dichotomy property for two generalized Rademacher–Riesz product measures μ, ν that either μ, ν are equivalent measures or they are mutually singular according as a certain series converges or diverges. We further give sufficient conditions so that in the equivalence case the Radon–Nikodym derivative dμ/dν belongs to Lp(v) for all positive real numbers p, by proving that a certain product martingale converges in Lp(v) for p ≧ 1.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 2 , June 1994 , pp. 243 - 254
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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