Constructive k-Additive Measure and Decreasing Convergence Theorems.

Pan and concave integrals are division-type nonlinear integrals defined on a monotone measure space. These satisfy the monotone increasing convergence theorem under reasonable conditions. However, the monotone decreasing convergence theorem for these integrals was proved only under limited conditions. In this study we consider the k-additive monotone measure on a non-discrete measurable space, and argue this property of Pan and concave integrals on a k-additive monotone measure space.