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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