@article{theextendedvillesinequalityfor,
  title = {The extended Ville's inequality for nonintegrable nonnegative supermartingales},
  author = {Hongjian Wang and Aaditya Ramdas},
  year = {2023},
  eprint = {2304.01163},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2304.01163v3},
}