An Abstract Law of Large Numbers, Sankhya
We study independent random variables (Zi)i∈I aggregated by integrating with respect to a nonatomic and finitely additive probability over the index set I. We analyze the behavior of the resulting random average and establish that any measure that guarantees the measurability of integral satisfies a strong form of the law of large numbers.
Nabil Al-Najjar, Luciano Pomatto
Al-Najjar, Nabil, and Luciano Pomatto. 2019. An Abstract Law of Large Numbers. Sankhya. 80: 1-12.