loss function

let $\text{[math]}$ be a measurable space and $\text{[math]}$ be a closed subset. then a function $\text{[math]}$ is called a loss function, or simply a loss, if it is measurable.

we will interpret $\text{[math]}$ as the cost, or loss, of predicting $\text{[math]}$ by $\text{[math]}$ if $\text{[math]}$ is observed, i.e., the smaller the value $\text{[math]}$ is, the better $\text{[math]}$ predicts $\text{[math]}$ in the sense of $\text{[math]}$ . from this it becomes clear that constant loss functions, such as $\text{[math]}$ , are rather meaningless for our purposes, since they do not distinguish between good and bad predictions.
[cite:@svm_steinwart_2008 definition 2.1]