# Reference for Dudley's chaining integral

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

@ARTICLE{MR512411,
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:

@article{Dudley1967290,
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.