Autocontinuity and convergence theorems for the Choquet integral

We provide convergence theorems for the Choquet integral for various notions of convergence. Monotone almost uniform convergence from above/below is associated to monotone autocontinuity from above/below. The dominated almost uniform convergence is associated to monotone autocontinuity. Autocontinuity can be associated to the dominated convergence in measure, in mean or in strict-measure.