Covering numbers for real-valued function classes

We find tight upper and lower bounds on the growth rate for the covering numbers of functions of bounded variation in the /spl Lscr//sub 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 /spl Lscr//sub 1/(dP) metrics in terms of a scale-sensitive combinatorial dimension of the function class.