Central limit theorems for dependent variables. II
[For part I see Z. Wahrscheinlichkeitstheor. Verw. Geb. 57, 509-534 (1981; Zbl 0451.60027), Corrections ibid. 63, 555 (1983).] Two families of measures of the dependence between two random variables are introduced. They include the strong-mixing ''distance''. Two central limit theorems are proved for dependent samples or processes where the dependency on the ''past'' is not too strong. Tightness of the empirical process is shown to hold under conditions involving only the four- dimensional marginals of the sample.
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