Abstract
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.
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