We will continue the talk of 10.11. We will show two theorems left from 10.11 that $C(\beta N)$ has the Grothendieck property (this strengthens the nonexistence of nontrivial convergent sequences in $\beta N$) and the conditions equivalent to the Grothendieck property for $C(K)$ spaces. This naturally leads to considering the weak compactness in the space of measures and its characterizations.