Pacific Journal of Mathematics

Norm convergence of martingales of Radon-Nikodym derivatives given a $\sigma$-lattice.

R. B. Darst and G. A. DeBoth

Article information

Source
Pacific J. Math., Volume 40, Number 3 (1972), 547-552.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102968554

Mathematical Reviews number (MathSciNet)
MR0310965

Zentralblatt MATH identifier
0232.28006

Subjects
Primary: 60G45
Secondary: 28A45

Citation

Darst, R. B.; DeBoth, G. A. Norm convergence of martingales of Radon-Nikodym derivatives given a $\sigma$-lattice. Pacific J. Math. 40 (1972), no. 3, 547--552. https://projecteuclid.org/euclid.pjm/1102968554


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References

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  • [2] H. D. Brunk and S. Johansen, A generalized Radon-Nikodymderivative, Pacific J. Math., 34 (1970), 585-617.
  • [3] R. B. Darst, The Lebesgue decomposition, Radon-Nikodymderivative,conditional expectation and martingale convergence for lattices of sets, Pacific J. Math., 35(1970), 581-600.
  • [4] R. B. Darst and G.A. DeBoth, Two approximation properties and a Radon-Nikodym derivative for lattices of sets, Indiana Univ. Math. J., 21 (1971), 355-362.
  • [5] S. Johansen, The descriptive approach to the derivative of a set functionwith res pect to a -lattice, Pacific J. Math., 21 (1967), 49-58.
  • [6] M. A. Krasnoseskii and Ya. B. Rutickii, Convex functionsand Orlicz spaces (Translation), Groningen, 1961.
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  • [8] J. J. Uhl, Applicationsof Radon-Nikodymtheorems to martingaleconvergence, Trans. Amer. Math. Soc, 145 (1969), 271-285.
  • [9] J. J. Uhl. Jr., Martingalesof vector valued set functions,Pacific J. Math., 30 (1969), 533-548.