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Laws of large numbers of negatively correlated random variables for capacities. (English) Zbl 1260.28012
Summary: Our aim is to present some limit theorems for capacities. We consider a sequence of pairwise negatively correlated random variables. We obtain laws of large numbers for upper probabilities and 2-alternating capacities, using some results in classical probability theory and a non-additive version of Chebyshev’s inequality and a Borel-Cantelli lemma for capacities.
28C15Set functions and measures on topological spaces
28A12Contents, measures, outer measures, capacities
60F05Central limit and other weak theorems
60F15Strong limit theorems
91A44Games involving topology or set theory
Full Text: DOI
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