An elementary proof of the covariance inequality for Choquet integral

摘要

The covariance inequality, also known as Chebyshev's inequality, is a very important inequality in probability theory. In generalized measure theory, the proof of this inequality for Choquet integral has a long process. In this paper, we present a simple proof of Chebyshev's inequality for Choquet integral which requires only knowledge of some basic properties of Choquet integral. (C) 2015 Elsevier B.V. All rights reserved.