衰变下的熵
Entropy under disintegrations
摘要：
本文考虑任意可测空间上概率测度关于给定的$σ$ -有限参考测度绝对连续的微分熵。我们的渐近均分财产在这种一般情况下，结果是民间传说的一部分，但我们的介绍在一定程度上是新颖的。然后，我们研究了一个一般框架下，这样的熵满足链规则：措施的解体。在这种情况下，我们给出了条件熵的渐近解释。最后，我们将所得结果应用于典型关系中的Haar测度.
英文摘要：
We consider the differential entropy of probability measures absolutely continuous with respect to a given $σ$-finite reference measure on an arbitrary measurable space. We state the asymptotic equipartition property in this general case; the result is part of the folklore but our presentation is to some extent novel. Then we study a general framework under which such entropies satisfy a chain rule: disintegrations of measures. We give an asymptotic interpretation for conditional entropies in this case. Finally, we apply our result to Haar measures in canonical relation.
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