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.


28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
28A12 Contents, measures, outer measures, capacities
60F05 Central limit and other weak theorems
60F15 Strong limit theorems
91A44 Games involving topology, set theory, or logic
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