Reference for Dudley's chaining integral
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.