For a map of the unit interval with an indifferent fixed point, we prove anupper bound for the variance of all observables of $n$ variables$K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based oncoupling and decay of correlation properties of the map. We then give variousapplications of this inequality to the almost-sure central limit theorem, thekernel density estimation, the empirical measure and the periodogram.
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机译：对于一个固定点无关紧要的单位区间图，我们证明了所有可观测变量$ n $变量$ K：[0,1] ^ n \ to \ R $的方差Lipschitz的上界。该证明基于地图相关属性的耦合和衰减。然后，我们将这种不等式的各种应用应用于几乎确定的中心极限定理，核密度估计，经验测度和周期图。
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