The convergence of hulls of curves

It is shown that a simple closed curve in $${\mathbb {C}}^n$$ uniform limit of rectifiable curves each which has nontrivial polynomial hull itself hull. In case the rectifiable, to be hulls. also every , $$n\ge 2$$ can approximated total variation norm by polynomially convex, coincides with original except on an arbitrarily small segment. As corollary, it arc contained curve.