  The main goal of this work is to prove an instance of the unique continuation
principle for area minimizing integral currents. More precisely, consider an
$m$-dimensional area minimizing integral current and an $m$-dimensional minimal
surface, both contained in $\mathbb{R}^{n+m}$ with $n\geq 1$. We show that if,
in an integral sense, the current has infinite order of contact with the
minimal surface at a point, then the current and the minimal surface coincide
in a neighborhood of that point.
