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Transactions of the American Mathematical Society

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A Radon-Nikoým theorem for operator-valued measures


Author: Hugh B. Maynard
Journal: Trans. Amer. Math. Soc. 173 (1972), 449-463
MSC: Primary 28A45; Secondary 46G10
DOI: https://doi.org/10.1090/S0002-9947-1972-0310187-4
MathSciNet review: 0310187
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Abstract: The purpose of this paper is to obtain a characterization of indefinite integrals of vector-valued functions with respect to countably additive operator-valued measures with finite variation. This result is then specialized to several simpler situations.


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  • [1] N. Dinculeanu, Vector measures, Internat. Series of Monographs in Pure and Appl. Math., vol. 95, Pergamon Press, Oxford; VEB Deutscher Verlag der Wissenschaften, Berlin, 1967. MR 34 #6011b. MR 0206190 (34:6011b)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [3] M. Métivier, Martingales à valeurs vectorielles. Applications à la dérivation des mesures vectorielles, Ann. Inst. Fourier (Grenoble) 17 (1967), fasc. 2, 175-208. MR 40 #926. MR 0247663 (40:926)
  • [4] M. A. Rieffel, The Radon-Nikodým theorem for the Bochner integral, Trans. Amer. Math. Soc. 131 (1968), 466-487. MR 36 #5297. MR 0222245 (36:5297)
  • [5] -, Dentable subsets of Banach spaces, with application to a Radon-Nikodým theorem, Proc. Conference Functional Analysis (Irvine, Calif., 1966), Academic Press, London; Thompson, Washington, D. C., 1967, pp. 71-77. MR 36 #5668. MR 0222618 (36:5668)
  • [6] J. J. Uhl, Jr., Applications of Radon-Nikodým theorems to martingale convergence, Trans. Amer. Math. Soc. 145 (1969), 271-285. MR 40 #4983. MR 0251756 (40:4983)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0310187-4
Keywords: Radon-Nikodým theorem, operator-valued measures, Bochner integral
Article copyright: © Copyright 1972 American Mathematical Society

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