Dudley's chaining integral is commonly used to bound Rademacher complexities. I recall seeing several papers give this as the reference

  author = {Dudley, R. M.},
  title = {Central limit theorems for empirical measures},
  journal = {Ann. Probab.},
  year = {1978},
  volume = {6},
  pages = {899--929 (1979)},
  number = {6},
  coden = {APBYAE},
  fjournal = {The Annals of Probability},
  issn = {0091-1798},
  mrclass = {60F05 (28C20 60B10 60F17)},
  mrnumber = {MR512411 (81k:60029a)},
  mrreviewer = {P. R{\'e}v{\'e}sz}

but I don't think the result in question actually appears in that paper. Could anyone point me to the definitive reference?


I think the proper reference is:

    Author = {R.M Dudley},
    Doi = {http://dx.doi.org/10.1016/0022-1236(67)90017-1},
    Issn = {0022-1236},
    Journal = {Journal of Functional Analysis},
    Number = {3},
    Pages = {290 - 330},
    Title = {The sizes of compact subsets of Hilbert space and continuity of Gaussian processes},
    Url = {http://www.sciencedirect.com/science/article/pii/0022123667900171},
    Volume = {1},
    Year = {1967},
    Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0022123667900171},
    Bdsk-Url-2 = {http://dx.doi.org/10.1016/0022-1236(67)90017-1}}

See Theorem 3.1. for the relevant result, although stated in terms of continuity of Gaussian processes.


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