Similar facts hold about weak dominance, though the situation is more subtle. The crucial observation is that there is a characterization of weak dominance in terms of best response to certain types of probability measures. A probability measure \(p\in \Delta(X)\) is said to have full support (with respect to \(X\)) if \(p\) assigns positive probability to every element of \(X\) (formally, \(supp(p)=\{x\in X \mid p(x)&gt;0\}=X\)). Let \(\Delta^{&gt;0}(X)\) be the set of full support probability measures on \(X\). A full support probability on \(S_{-i}\) means that player \(i\) does not completely rule out (in the sense, that she assigns zero probability to) any strategy profiles of her opponents. The following analogue of Lemma 3.1 is also well-known: