On the Existence of the Augustin Mean

@article{Cheng2021OnTE,
  title={On the Existence of the Augustin Mean},
  author={Hao-Chung Cheng and Barış Nakiboğlu},
  journal={2021 IEEE Information Theory Workshop (ITW)},
  year={2021},
  pages={1-6}
}
The existence of a unique Augustin mean and its invariance under the Augustin operator are established for arbitrary input distributions with finite Augustin information for channels with countably generated output $\sigma$-algebras. The existence is established by representing the conditional Rényi divergence as a lower semi-continuous and convex functional in an appropriately chosen uniformly convex space and then invoking the Banach-Saks property in conjunction with the lower semi-continuity… 

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