Abstract
If (X,T) is a measure-preserving system, \( \alpha \) a nontrivial partition of X into two sets and f a positive increasing function defined on the positive real numbers, then the limit inferior of the sequence \( \{2H(\alpha_{0}^{n-1})/f(n)\}_{n=1}^{\infty} \) is greater than or equal to the limit inferior of the sequence of quotients of the average complexity of trajectories of length n generated by \( \alpha_{0}^{n-1} \) and nf(log2(n))/log2(n). A similar statement also holds for the limit superior.
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