A remark on Vapnik-Chervonienkis classes

• Autorzy: Agata Smoktunowicz
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 74
• Numer: 1
• Strony: 93-98

Daty

wydano

1997

otrzymano

1996-11-05

poprawiono

1996-12-02

Twórcy

autor

Agata Smoktunowicz

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] R. M. Dudley, Uniform Central Limit Theorems, Cambridge University Press, to appear.
• [2] P. Erdős and G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1939), 463-470.
• [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.
• [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.