0000000001040448
AUTHOR
Kazimierz Musial
Integration of multifunctions with closed convex values in arbitrary Banach spaces
Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We pay particular attention to the "positive multifunctions". Among them an investigation of multifunctions determined by vector-valued functions is presented. Finally, decomposition results are obtained for scalarly and gauge-defined integrals of multifunctions and a full description of McShane integrability in terms of Henstock and Pettis integrability is given.
Convergence for varying measures in the topological case
In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.
Convergence for varying measures
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.