Here mu is a set of measurements, the phi are sections of mu (one for each i in {1,2, ..., K}) thought of as parametrizations, and e is a real classification to be estimated. It is pretty easy to show that the average success rate of the estimator is the sum of the volumes of the Vi intersected with the inverse image of i under e( ). So when X has measure 1, the total error is:

I guess it makes sense to call this a

**best model estimate**.