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On limit theorems for random fields. (English) Zbl 1343.60010

Summary: A complete separable metric space of functions defined on the positive quadrant of the plane is constructed. The characteristic property of these functions is that at every point \(x\) there exist two lines intersecting at this point such that limits \(\lim_{y\to x}f(y)\) exist when \(y\) approaches \(x\) along any path not intersecting these lines. A criterion of compactness of subsets of this space is obtained.

MSC:

60F05 Central limit and other weak theorems
60G60 Random fields
54C35 Function spaces in general topology
54E45 Compact (locally compact) metric spaces
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