A Mahler measure on hyperelliptic curves

We discuss a Mahler measure-type canonical height on hyperelliptic curves, generalising
the Neron-Tate height on elliptic curves. The canonical height is non-negative, and vanishes precisely on torsion points. We will discuss how
local equidistribution results for integrals appearing in the definition of
the canonical height have a bearing on questions of finiteness of integral
points, and state such an equidistribution result.