let be a measurable space and be a closed subset. then a function is called a loss function, or simply a loss, if it is measurable.
we will interpret as the cost, or loss, of predicting by if is observed, i.e., the smaller the value is, the better predicts in the sense of . from this it becomes clear that constant loss functions, such as , are rather meaningless for our purposes, since they do not distinguish between good and bad predictions.