Sumset and Inverse Sumset Theory for Shannon Entropy

@article{Tao2010SumsetAI,
  title={Sumset and Inverse Sumset Theory for Shannon Entropy},
  author={Terence Tao},
  journal={Combinatorics, Probability & Computing},
  year={2010},
  volume={19},
  pages={603-639}
}
Let G = (G, +) be an additive group. The sumset theory of Plünnecke and Ruzsa gives several relations between the size of sumsets A + B of finite sets A, B, and related objects such as iterated sumsets kA and difference sets A − B, while the inverse sumset theory of Freiman, Ruzsa, and others characterises those finite sets A for which A + A is small. In this paper we establish analogous results in which the finite set A ⊂ G is replaced by a discrete random variable X taking values in G, and… CONTINUE READING

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