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In Chapter 6 , we defined \(h(T,\alpha )\) as information growth associated with the sequence of partitions \(\vee _0^{n-1} T^{-i} \alpha \) as n increases. Since \(H(\cdot )\) can be seen as the spatial average of an information function, a complementary view is to characterize entropy as information growth along individual trajectories. That is what this chapter is about.

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The Shannon-McMillan-Breiman Theorem

  • 章节

  • 发表日期：

    2026年

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  • Alex Blumenthal,
  • Lai-Sang Young

摘要

In Chapter 6 , we defined \(h(T,\alpha )\) as information growth associated with the sequence of partitions \(\vee _0^{n-1} T^{-i} \alpha \) as n increases. Since \(H(\cdot )\) can be seen as the spatial average of an information function, a complementary view is to characterize entropy as information growth along individual trajectories. That is what this chapter is about.