Abstract
We deal with a class of integrals of [0,1]-valued functions with respect to a probability measure induced by a copula. Since the original definition of the integral is not suitable for its direct computation, we focus on computational aspects using the standard technique of interchanging the integral and the derivative and give a relationship to a partial derivative of the copula. We also exemplify this approach for copulas containing singular support. Via the Markov kernel technique, we characterize all the copulas for which strict and weak versions of the integrals coincide by measuring the set of the intersection of the graph of the survival function and the support of a singular part of the copula.
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