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A remark on Vapnik-Chervonienkis classes. (English) Zbl 0892.60014

Summary: We show that the family of all lines in the plane, which is a VC class of index 2, cannot be obtained in a finite number of steps starting with VC classes of index 1 and applying the operations of intersection and union. This confirms a common belief among specialists and solves a question asked by several authors.

MSC:

60C05 Combinatorial probability
60F99 Limit theorems in probability theory
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