Hereditary Hsu-Robbins-Erdös Law of Large Numbers

Istvan Berkes, Ioannis Karatzas, Walter Schachermayer

We show that every sequence $f_1,f_2,\cdots$ of real-valued random variables with $\sup_{n \in \N} \E (f_n^2) < \infty$ contains a subsequence $f_{k_1},f_{k_2},\cdots$ convergi…