On superpositionally measurable multifunctions
Andrzej Spakowski (1989)
Acta Universitatis Carolinae. Mathematica et Physica
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Andrzej Spakowski (1989)
Acta Universitatis Carolinae. Mathematica et Physica
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Wojciech Zygmunt (1992)
Commentationes Mathematicae Universitatis Carolinae
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For multifunctions , measurable in the first variable and semicontinuous in the second one, a relation is established between being product measurable and being superpositionally measurable.
C. J. Himmelberg, F. S. Van Vleck (1972)
Rendiconti del Seminario Matematico della Università di Padova
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Beata Kubiś (2001)
Mathematica Bohemica
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We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets.
Diego Averna, Salvatore A. Marano (1999)
Rendiconti del Seminario Matematico della Università di Padova
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Hess, Christian (1995)
Journal of Convex Analysis
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Andrzej Nowak, Celina Rom (2006)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Let F be a multifunction from a metric space X into L¹, and B a subset of X. We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F(x) for x ∈ B.
Gabriele Bonanno (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.