Laws of large numbers without additivity

Terán, Pedro

doi:10.1090/S0002-9947-2014-06053-4

Laws of large numbers without additivity
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by Pedro Terán PDF

Trans. Amer. Math. Soc. 366 (2014), 5431-5451

Abstract:

The law of large numbers is studied under a weakening of the axiomatic properties of a probability measure. Averages do not generally converge to a point, but they are asymptotically confined in a limit set for any random variable satisfying a natural ‘finite first moment’ condition. It is also shown that their behaviour can depart strikingly from the intuitions developed in the additive case.

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