For all questions involving utility functions as used in economics and decision theory, including study of their properties or how they can be used to represent preferences.
A utility function is a numerical representation of an agent’s preferences. If $\succeq$ is a preference relation on a set of alternatives $X$, then the function $u: X\to\mathbb{R}$ is a utility representation of $\succeq$ if $x\succeq y$ holds if and only if $u(x)\ge u(y)$. In many cases, one might want the representation to be of a special form. For example, if $X$ is the set of probability distributions on a finite set $F=\{y_1,\ldots,y_n\}$ so that $x=(p_1,\ldots,p_n)$, then an expected utility representation of $\succeq$ is of the form $$u(x)=\sum_{i=1}^n p_iv(y_i)$$ for some function $v:F\to\mathbb{R}$.
