# A remark on Vapnik-Chervonienkis classes

Colloquium Mathematicae (1997)

- Volume: 74, Issue: 1, page 93-98
- ISSN: 0010-1354

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topSmoktunowicz, Agata. "A remark on Vapnik-Chervonienkis classes." Colloquium Mathematicae 74.1 (1997): 93-98. <http://eudml.org/doc/210504>.

@article{Smoktunowicz1997,

abstract = {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.},

author = {Smoktunowicz, Agata},

journal = {Colloquium Mathematicae},

keywords = {Vapnik-Chervonienkis classes},

language = {eng},

number = {1},

pages = {93-98},

title = {A remark on Vapnik-Chervonienkis classes},

url = {http://eudml.org/doc/210504},

volume = {74},

year = {1997},

}

TY - JOUR

AU - Smoktunowicz, Agata

TI - A remark on Vapnik-Chervonienkis classes

JO - Colloquium Mathematicae

PY - 1997

VL - 74

IS - 1

SP - 93

EP - 98

AB - 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.

LA - eng

KW - Vapnik-Chervonienkis classes

UR - http://eudml.org/doc/210504

ER -

## References

top- [1] R. M. Dudley, Uniform Central Limit Theorems, Cambridge University Press, to appear. Zbl0951.60033
- [2] P. Erdős and G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1939), 463-470. Zbl0012.27010
- [3] J. Hoffmann-Jοrgensen, K.-L. Su and R. L. Taylor, The law of large numbers and the Ito-Nisio theorem for vector valued random fields, J. Theoret. Probab. 10 (1997), 145-183. Zbl0870.60006
- [4] S. Kwapień, On maximal inequalities for sums of independent random variables, in: XIII Jubileuszowy Zjazd Matematyków Polskich, Referaty, Wydawnictwa PTM, 1994 (in Polish).
- [5] M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, 1991.

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