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math.DS2017★ 5 cited
Local conditional entropy in measure for covers with respect to a fixed partition
Pierre Paul Romagnoli
In this paper, we introduce two measure theoretical notions of conditional entropy for finite measurable covers conditioned to a finite measurable partition and prove that they are…
math.DS2015
Shearer's inequality and Infimum Rule for Shannon entropy and topological entropy
Tomasz Downarowicz, Bartosz Frej, Pierre-Paul Romagnoli
We review subbadditivity properties of Shannon entropy, in particular, from the Shearer's inequality we derive the "infimum rule" for actions of amenable groups. We briefly discuss…