Shannon entropy convergence results in the countable infinite case

@article{Silva2012ShannonEC,
  title={Shannon entropy convergence results in the countable infinite case},
  author={Jorge F. Silva and Patricio Parada},
  journal={2012 IEEE International Symposium on Information Theory Proceedings},
  year={2012},
  pages={155-159}
}
The convergence of the Shannon entropy in the countable infinity case is revisited and extended in this work. New results are presented that provide necessary and sufficient conditions for the convergence of the entropy in different settings, including scenarios with both finitely and infinitely supported measures. These results show some connections between the Shannon entropy convergence and the convergence in information divergence. 

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