A note on a scale-sensitive dimension of linear bounded functionals in Banach Spaces

  • Leonid Gurvits
Session 9
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1316)


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 restrited 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.


VC-dimension scale-sensitive dimension Banach Spaces 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Leonid Gurvits
    • 1
    • 2
  1. 1.NEC Research InstitutePrinceton
  2. 2.DIMACSRutgers UniversityNew Brunswick

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