Abstract:We will use continuum-theory to obtain an upper bound for the Kolmogorov-Sinai metric entropy. This bound (throughout called continuum-wise entropy) though different satisfies some properties resembling the metric entropy. Moreover, we prove that every ergodic measure with positive continuum-wise entropy is continuum-wise expansive.

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中文翻译：

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连续论的熵界

摘要：我们将使用连续论来获得Kolmogorov-Sinai度量熵的上限。尽管不同，但这个边界（通称为连续性熵）满足一些类似于度量熵的性质。此外，我们证明具有正连续统熵的每个遍历测度都是连续统可扩展的。

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