# THE HOFFMANN-JORGENSEN INEQUALITY IN METRIC SEMIGROUPS

```@article{Khare2017THEHI,
title={THE HOFFMANN-JORGENSEN INEQUALITY IN METRIC SEMIGROUPS},
author={Apoorva Khare and Bala Rajaratnam},
journal={Annals of Probability},
year={2017},
volume={45},
pages={4101-4111}
}```
• Published 7 October 2016
• Mathematics
• Annals of Probability
We prove a refinement of the inequality by Hoffmann-Jorgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in the Banach space literature, including those by Johnson and Schechtman Ann. Probab. 17 (1989) 789-808], Klass and Nowicki Ann. Probab. 28 (2000) 851-862], and Hitczenko and Montgomery-Smith Ann. Probab. 29 (2001) 447-466]. Finally, we show that the Hoffmann…
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