Abstract
There is given an overview of generalizations of the integral inequalities for integrals based on nonadditive measures. The Holder, Minkowski, Jensen, Chebishev and Berwald inequalities are generalized to the Choquet and Sugeno integrals. A general inequality which cover Holder and Minkowski type inequalities is considered for the universal integral. The corresponding inequalities for important cases of the pseudo-integral and applications of these inequalities in pseudo-probability are also given.
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