Sibony and Wong [34] have been first in showing that if a compact subset $K$ of $\mathbb{C}\mathbb{P}^{n}$ is large enough then the polynomial hull of $K_{0}$ contains a full neighborhood of the origin in $\mathbb{C}^{n+1}$. They used the (complicated) notion of $\Gamma$-capacity. Their approach has been simplified by Alexander [1] who introduced a projective capacity which is comparable to $T_{\omega}$ (see theorem 4.4 in [1]). The proof given above is essentially Alexander’s (see also theorem 4.3 in [36]).

This result has been used recently in complex dynamics (see [17],[23]).