A Weak Law of Large Numbers for Dependent Random Variables

Ioannis Karatzas, Walter Schachermayer

Every sequence $f_1,f_2,\cdots$ of random variables with ${\lim }_{M\to \infty }(M{\sup }_{k\in \mathbb{N}}\mathbb{P}(|f_k|>M))=0$ contains a subsequence $…