This paper concerns the folklore statement that “entropy is a lower bound for compression.” More precisely, we derive from the entropy theorem a simple proof of a pointwise inequality first stated by Ornstein and Shields and which is the almost-sure version of an average inequality first stated by Khinchin in 1953. We further give an elementary proof of the original Khinchin inequality, which can be used as an exercise for information theory students, and we conclude by giving historical and technical notes of such inequality.

中文翻译：

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熵和压缩：Khinchin-Ornstein-Shields不等式的简单证明

本文关注的民间传说是“熵是压缩的下界”。更准确地说，我们从熵定理中得出关于Ornstein和Shields首次提出的点不等式的简单证明，这是Khinchin于1953年首先提出的平均不等式的几乎确定的版本。我们进一步给出了原始证明的基本证明。 Khinchin不等式可以用作信息论系学生的练习，最后我们给出此类不等式的历史和技术说明。