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This paper concerns the folklore statement that ``entropy is a lower boundfor compression''. More precisely we derive from the entropy theorem a simpleproof of a pointwise inequality firstly stated by Ornstein and Shields andwhich is the almost-sure version of an average inequality firstly stated byKhinchin in 1953. We further give an elementary proof of original Khinchininequality that can be used as an exercise for Information Theory students andwe conclude by giving historical and technical notes of such inequality.

Entropy and Compression: A simple proof of an inequality of Khinchin-Ornstein-Shields