Abstract. Let $w(x):=\exp(-Q(x))$ be a non-negative weight function on the closed set $\Sigma\subset {\msbm R}$. We will introduce some conditions, each of which guarantees that the support of the equilibrium measure associated with $w$ is an interval. For example: if $\exp(Q(x))$ is convex, then the support of the equilibrium measure is an interval. These type of conditions are very useful when determining the equilibrium measure. An integral representation formula for the equilibrium measure is also given.

AMS Subject Classification (1991): 31A15

Received September 22, 2003, and in revised form November 28, 2003. (Registered under 5797/2009.)