A function $d: \chi \times \hat{\chi} \rightarrow \mathbb{R}^+$

from the set of source alphabet ($\chi$)– reproduction alphabet ($\hat{\chi}$) into the set of nonnegative Real numbers. The distortion $d(x, \hat{x})$ is a measure of the cost of representing the symbol $x$ by the symbol $\hat{x}$, used in Rate-distortion theory.

See page 304 in Cover&Thomas