On Choquet-Pettis Expectation of Banach-Valued Functions: A Counter Example

0491734 - ÚTIA 2019 RIV SG eng J - Journal Article
Agahi, H. - Mesiar, Radko
On Choquet-Pettis Expectation of Banach-Valued Functions: A Counter Example.
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems. Roč. 26, č. 2 (2018), s. 255-259. ISSN 0218-4885. E-ISSN 1793-6411
Institutional support: RVO:67985556
Keywords : Choquet expectation * Pettis integral * vector space
OECD category: Pure mathematics
Impact factor: 1.286, year: 2018
http://library.utia.cas.cz/separaty/2018/E/mesiar-0491734.pdf

In probability theory, mathematical expectation of a random variable is very important. Choquet expectation (integral), as a generalization of mathematical expectation, is a powerful tool in various areas, mainly in generalized probability theory and decision theory. In vector spaces, combining Choquet expectation and Pettis integral has led to a challenging and an interesting subject for researchers. In this paper, we indicate and discuss a failure in the previous definition of Choquet-Pettis integral of Banach space- valued functions. To obtain a correct definition of Choquet-Pettis integral, an open problem concerning the linearity of the Choquet integral is stated.
Permanent Link: http://hdl.handle.net/11104/0285672