2022/06/26 by Kaliaj, Sokol Bush
#28B05 #28B20 #46A03 #46A13 #46B22 #46G10 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2206.12936
In this paper we define the Radon-Nikodym class (RN class) of locally convex topological vector spaces. The RN class is characterized in terms of the Radon-Nikodym theorem for vector measures using integrable by seminorm derivatives. It is shown that the RNP class of all complete Hausdorff locally convex spaces possessing the Radon-Nikodym property is properly contained in the RN class. As an application we present a Radon-Nikodym theorem for multimeasures with respect to the Pettis integrable multifunctions in terms of the RN class.