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}
}
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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