Autocontinuity and convergence theorems for the Choquet integral

Authors:
Yann Rébillé
Affiliations:
LEMNA, Institute of Economics and Management of Nantes-IAE, chemin la Censive du Tertre, BP 62232, 44322 Nantes Cedex 3, France
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

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.