Radon-Nikodym property for vector-valued integrable functions
Khurana, Surjit Singh
Annales de l'Institut Fourier, Tome 28 (1978), p. 203-208 / Harvested from Numdam
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On montre que si un espace de Fréchet E a la propriété de Radon-Nikodym, alors L p (E,ν) la possède aussi, pour 1<p<∞.

It is proved that if a Frechet space E has R-N property, then L p (E,ν) also has R-N property, for 1<p<∞.

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     author = {Khurana, Surjit Singh},
     title = {Radon-Nikodym property for vector-valued integrable functions},
     journal = {Annales de l'Institut Fourier},
     volume = {28},
     year = {1978},
     pages = {203-208},
     doi = {10.5802/aif.709},
     mrnumber = {80f:46043},
     zbl = {0353.46023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1978__28_3_203_0}
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Khurana, Surjit Singh. Radon-Nikodym property for vector-valued integrable functions. Annales de l'Institut Fourier, Tome 28 (1978) pp. 203-208. doi : 10.5802/aif.709. http://gdmltest.u-ga.fr/item/AIF_1978__28_3_203_0/

[1] J. Diestel, J.J. Uhl, Jr., The Radon-Nikodym property for Banach space valued measures, Rocky Mountain J. Math., 6 (1976), 1-46. | Zbl 0339.46031

[2] L. Drewnowski, Topological rings of sets, continuous set functions, integration I, II, III, Bull. Acad. Polon. Sci., Ser. Math. Astron. Phys., 20 (1972), 269-276, 277-286, 439-445. | Zbl 0249.28004

[3] E. Saab, Dentabilité, points extrémaux et propriété de Radon-Nikodym, Bull. Soc. Math., 99 (1975), 129-134. | Zbl 0325.46036

[4] E. Saab, Dentabilité, points extrémaux et propriété de Radon-Nikodym, C.R. Acad. Sci., Paris, 280 (1975), 575-577. | Zbl 0295.46068

[5] H.H. Schaefer, Topological vector spaces, Macmillan, New York (1971). | MR 49 #7722 | Zbl 0217.16002

[6] K. Sundaresan, The Radon-Nikodym theorem for Lebesgue-Bochner function spaces, J. Func. Anal., 24 (1977), 276-279. | MR 56 #9246 | Zbl 0341.46019

[7] Ju. B. Tumarkin, On locally convex spaces with basis, Doklady Acad. Sci. USSR, 195 (1970), 1278-1281, English Translation : Soviet Math., 11 (1970), 1672-1675. | Zbl 0216.40701

[8] P. Turpin, Convexité dans les espaces vectoriels topologiques généraux, Disser. Math., 131 (1976). | MR 54 #11028 | Zbl 0331.46001