Autocontinuity and convergence theorems for the Choquet integral

Yann Rébillé (1)

1 LEMNA - Laboratoire d'économie et de management de Nantes Atlantique

Our aim is to provide some convergence theorems for the Choquet integral with respect to various notions of convergence. For instance, the dominated convergence theorem for almost uniform convergence is related to autocontinuous set functions. Autocontinuity can also be related to convergence in measure, strict convergence or mean convergence. Whereas the monotone convergence theorem for almost uniform convergence is related to monotone autocontinuity, a weaker version than autocontinuity.

Domaines: Economies et finances; Gestion et management

Yann Rébillé. Autocontinuity and convergence theorems for the Choquet integral. 2009. ⟨hal-00422562⟩