The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the R ̊adstr ̈om embedding theorem.
Labuschagne, C., Marraffa, V. (2011). On spaces of Bochner and Pettis integrable functions and their set-valued counterparts. In S. LI, X. WANG, Y. OKAZAKI, J. KAWABE, T. MUROFUSHI, L. GUAN (a cura di), Nonlinear Mathematics for Uncertainty and its Applications (pp. 51-59) [10.1007/978-3-642-22833-9_6].
On spaces of Bochner and Pettis integrable functions and their set-valued counterparts
MARRAFFA, Valeria
2011-01-01
Abstract
The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the R ̊adstr ̈om embedding theorem.
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