Relaxation theorem for set-valued functions with decomposable values

• Autorzy: Andrzej Kisielewicz
• Języki publikacji: EN

Abstrakty

EN

Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has $fχ_A + gχ_{T\A} ∈ K$. Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.

Słowa kluczowe

EN

set-valued function; continuous selection; fixed point; decomposability; set-valued stochastic processes

Kategorie tematyczne

• 54C60: Set-valued maps
• 54C65: Selections

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1996
• Tom: 16
• Numer: 1
• Strony: 91-97

Daty

wydano

1996

Twórcy

autor

Andrzej Kisielewicz

• Institute of Mathematics, Technical University, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

• [1] N. Dunford, J.T. Schwartz, Linear Operators I, Int. Publ. INC., New York 1967.
• [2] F. Hiai and H. Umegaki, Integrals, conditional expections and martingals of multifunctions, J. Multivariate Anal., 7 (1977), 149-182.
• [3] A. Kisielewicz, Selection theorem for set-valued function with decomposable values, Comm. Math., 34 (1994), 123-135.