Covering numbers for real-valued function classes

P. L. Bartlett, S. R. Kulkarni, S. E. Posner

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


We find tight upper and lower bounds on the growth rate for the covering numbers of functions of bounded variation in the 1 metric in terms of all the relevant constants. We also find upper and lower bounds on covering numbers for general function classes over the family of 1(dP) metrics in terms of a scale-sensitive combinatorial dimension of the function class.

Original languageEnglish (US)
Pages (from-to)1721-1724
Number of pages4
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Bounded variation
  • Covering numbers
  • Fat-shattering dimension
  • Metric entropy
  • Scale-sensitive dimension
  • VC dimension

Cite this