We consider the problem of finding conditions under which an \(\alpha\)-coupling is possible for several random variables \(X_1,X_2,\ldots,X_k\) with a finite or countably infinite range of values and with given probability distributions, i.e., the possibility of constructing a joint distribution of these random variables such that \(\Pr\{X_1=X_2=\ldots=X_k\}=\alpha\).

中文翻译：

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几个随机变量的耦合

我们考虑寻找条件的问题，在这些条件下，几个随机变量\(X_1,X_2,\ldots,X_k\)具有有限或可数无限范围的值并且具有给定的概率分布，即构造这些随机变量的联合分布的可能性使得\(\Pr\{X_1=X_2=\ldots=X_k\}=\alpha\)。