  We study metric and analytic properties of generalized lemniscates
E_t(f)={z:ln|f(z)|=t}, where f is an analytic function. Our main result states
that the length function |E_t(f)| is a bilateral Laplace transform of a certain
positive measure. In particular, the function ln|E_t(f)| is convex on any
interval free of critical points of ln|f|. As another application we deduce
explicit formulas of the length function in some special cases.
