Convergence in Measure Theorems of the Choquet Integral Revisited

Abstract

The validity of the monotone convergence theorem, the Fatou and the reverse Fatou lemmas, and the dominated convergence theorem of the Choquet integral of measurable functions converging in measure are fully characterized by the conditional versions of the monotone autocontinuity and the autocontinuity. In those theorems the nonadditive measure may be infinite and the functions may be unbounded. The dual measure forms and the extension to symmetric and asymmetric Choquet integrals are also discussed.