1) If $K\subset K^{\prime}\subset X$ are Borel subsets then

2) If $K_{j}$ are Borel subsets of $X$ then $Cap_{\omega}(\cup K_{j})\leq\sum Cap_{\omega}(K_{j})$. Moreover $Cap_{\omega}(\cup K_{j})=\lim Cap_{\omega}(K_{j})$ if $K_{j}\subset K_{j+1}$.

3) If $\omega_{1}\leq\omega_{2}$ then $Cap_{\omega_{1}}(\cdot)\leq Cap_{\omega_{2}}(\cdot)$. For all $A\geq 1$, $Cap_{\omega}(\cdot)\leq Cap_{A\omega}(\cdot)\leq A^{n}Cap_{\omega}(\cdot)$. In particular if $\omega,\omega^{\prime}$ are two Kähler forms then there exists $C\geq 1$ such that

4) If $f:X\rightarrow X$ is holomorphic then for all Borel subset $K$ of $X$,

In particular $Cap_{\omega}(f(K))=Cap_{\omega}(K)$ for every $\omega$-isometry $f$.