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In classical measure theory, the Radon-Nikodym theorem states in a concise condition, namely domination, how a measure can be factorized by another (bounded) measure through a density function. Several approaches have been undertaken to see under which conditions an exact factorization can be obtained with set functions that are not σ-additive (for instance… (More)
We prove for outer continuous belief measures defined on compact spaces strong and weak laws of large numbers as Kolmogorov’s one for measures. These results contribute to M. Marinacci’s (Journal of Economic Theory 84 (1999) 145-195) though with different methods.
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… (More)