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Some Remarks on Capacitary Integrals and Measure Theory (2302.11847v1)
Published 23 Feb 2023 in math.FA and math.AP
Abstract: We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and strong subadditivity independent of regularity assumptions on the capacity, as well as various forms of standard measure theoretic convergence theorems for these non-additive integrals, e.g. Fatou's lemma and Lebesgue's dominated convergence theorem.
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