Error measure and Hoeffding inequality

[v_venky]

In the 1st chapter when Hoeffding is used, the error measure is simple mismatch -- there is no penalty associated with the different flavors of mismatch as in error measures. Is there a version of Hoeffding which we could use with error measure as well? If so how does it look? I imagine the red balls would now have weights of some sort -- two types of red balls for the two kinds of errors in a binary classifier.