Subadditivity of harmonic hull capacity ($\mathrm{cap}({\bigcup }_j{K}_j)\le {\sum }_j\mathrm{cap}(K_j)$)

When a finite union is a compact H-hull, hitting that union before the real axis implies hitting at least one member before the real axis. The union bound followed by the defining limit proves subadditivity of harmonic capacity from infinity in the upper half-plane.