The limiting form of the Radon--Nikodym property is true for all Fr\'echet spaces
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 37 (2010), pp. 55-69

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In this paper, we propose a new limiting form of the Radon–Nikodym property for the Bochner integral. We prove that the limiting form holds for an arbitrary Fréchet space as opposed to an ordinary Radon–Nikodym property. We consider some applications in linear and nonlinear analysis.
@article{CMFD_2010_37_a4,
     author = {I. V. Orlov and F. S. Stonyakin},
     title = {The limiting form of the {Radon--Nikodym} property is true for all {Fr\'echet} spaces},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {55--69},
     publisher = {mathdoc},
     volume = {37},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2010_37_a4/}
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I. V. Orlov; F. S. Stonyakin. The limiting form of the Radon--Nikodym property is true for all Fr\'echet spaces. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 37 (2010), pp. 55-69. http://geodesic.mathdoc.fr/item/CMFD_2010_37_a4/