A set P ⊂ ℕ is called predictive if for any zero entropy finite-valued stationary process (Xi)i∈ℤ, X0 is measurable with respect to (X−i)i∈P. We know that ℕ is a predictive set. In this paper, we give sufficient conditions and necessary ones for a set to be predictive. We also discuss linear predictivity, predictivity among Gaussian processes and relate these to Riesz sets which arise in harmonic analysis.

中文翻译：

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预测集

一套磷 ⊂ ℕ如果对于任何零熵有限值平稳过程，则称为预测(X一世)一世∈ℤ,X0是可测量的(X-一世)一世∈磷. 我们知道ℕ是一个预测集。在本文中，我们给出了一个集合具有预测性的充分条件和必要条件。我们还讨论了线性预测、高斯过程之间的预测，并将这些与谐波分析中出现的 Riesz 集联系起来。