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Moments of vector measures and Pettis integrable functions

Miloslav Duchoň (2011)

Czechoslovak Mathematical Journal

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.

New extension of the variational McShane integral of vector-valued functions

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset G of m -dimensional Euclidean space m . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from m -dimensional closed non-degenerate intervals to open and bounded subsets of m . 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...

On Denjoy-Dunford and Denjoy-Pettis integrals

José Gámez, José Mendoza (1998)

Studia Mathematica

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 f : [ a , b ] c 0 which is not Pettis integrable on any subinterval in [a,b], while ʃ J f belongs to c 0 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...

Currently displaying 121 – 140 of 311