Question: [21] Let P be a computable probability mass function of m identically distributed random variables. Show that the analogue of Theorem 8.1.1 holds. In this

[21] Let P be a computable probability mass function of m identically distributed random variables. Show that the analogue of Theorem 8.1.1 holds. In this case, the entropy is proportional to m, but cP is O(log m).

Comments. Hint: use K(P) = O(log m) and a similar proof to Theorem 8.1.1.

Source: [T.M. Cover, P. G´acs, and R.M. Gray, Ann. Probab., 17:3(1989), 840–865].

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