An converse theorem for density functions

@article{Bernhardsson2002AnCT,
  title={An converse theorem for density functions},
  author={Bo Bernhardsson},
  journal={Proceedings of the 41st IEEE Conference on Decision and Control, 2002.},
  year={2002},
  volume={2},
  pages={1890-1891 vol.2}
}
It is proved that existence of a density function is both necessary and sufficient for almost global stability in a nonlinear system. 

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