On a strong law of large numbers for monotone measures

Recently, Maccheroni et al. [Maccheroni, F., Marinacci, M., 2005. A strong law of large numbers for capacities. Ann. Probab. 33, 1171–1178] have provided an extension of the strong law of large numbers of i.i.d random variables for capacities. In this paper, we formulate new versions of the strong law of large numbers based on a submodular continuous monotone measure without the independence condition.

► New versions of the strong law of large numbers for monotone measures are given.
► This paper improves the series of papers on the topic.
► Some generalizations of Borel–Cantelli’s lemmas are given.