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)-isomorphism 
doi:10.1016/S0304-3975(00)00134-1 
Copyright © 2001 Elsevier Science B.V. All rights reserved.
A note on a scale-sensitive dimension of linear bounded functionals in Banach spaces
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Available online 4 June 2001.
Abstract
We show that “B is of type p>1” is a necessary and sufficient condition for a learnability of a class of linear bounded functionals with norm 
1 restricted to the unit ball in Banach space B. On the way, we give very short probabilistic proof for Vapnik's result (Hilbert space and improved) and improve our result with Pascal Koiran for convex halls of indicator functions. The approach we use in this paper allows to connect various results about learnability and approximation.
Author Keywords: VC-dimension; Scale-sensitive dimension; Banach spaces
1 Research at Rutgers partially supported by the US Air Force Grant AFOSR-94-0293.
Correspondence address. NEC Research Institute, 4 Independence Way, Princeton, N5 08540, USA; email: gurvits@research.nj.nec.com
