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The space \(\tilde D_ k\) land weak convergence for the rectangle-indexed processes under mixing. (English) Zbl 0721.60037

The authors generalize the Skorokhod topology to a space of functions on a set of rectangles. They also establish weak convergence of the weighted empirical process indexed by rectangles under weak and strong mixing conditions.

MSC:

60F17 Functional limit theorems; invariance principles
60B10 Convergence of probability measures
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