Measures vectorielies, measures cylindriques et propriété de Radon-Nikodym
Conditions, under which the elements of a locally convex vector space are the moments of a regular vector-valued measure and of a Pettis integrable function, both with values in a locally convex vector space, are investigated.
We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset of -dimensional Euclidean space . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from -dimensional closed non-degenerate intervals to open and bounded subsets of . We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our...
The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function which is not Pettis integrable on any subinterval in [a,b], while belongs to for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dundord...