On the Extension of Set-Valued Set Functions
On the Extension of Set-Valued Set Functions
First the authors give some results on the extension of additive set-valued set functions defined on a ring of subsets. Then they prove a Carathéodory-Hahn-Kluvanek-type theorem for such functions. Related results for countably additive set-valued set functions were given by \textit{D. A. Kandilakis} [Proc. Am. Math. Soc. 116, 85-92 (1992; Zbl 0762.28012)] and \textit{X. Xue, L. Cheng, G. Li} and \textit{X. Yao} [Comment. Math. Univ. Carolinae 37, 269-284 (1996; Zbl 0885.28008)]. Finally, they study extensions of normal multimeasures and transition multimeasures defined on an algebra of subsets to the generated \(\sigma\)-algebra. In the proofs they extensively use previous results on multimeasures, e.g., in [\textit{C. Godet-Thobie}, ``Multimesures et multimesures de transition'', Ph.D. thesis, University of Paris (1975)].
- Stellenbosch University South Africa
transition multimeasure, set-valued set functions, 28B05, Extension, extension, 28B20, set-valued set function, Vector-valued set functions, measures and integrals, Set-valued set functions and measures; integration of set-valued functions; measurable selections, Vector-valued measures and integration, multimeasure, 510, 46G10
transition multimeasure, set-valued set functions, 28B05, Extension, extension, 28B20, set-valued set function, Vector-valued set functions, measures and integrals, Set-valued set functions and measures; integration of set-valued functions; measurable selections, Vector-valued measures and integration, multimeasure, 510, 46G10
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