For a solution \(x\) of (1) \(x'(t)\in\text{co}F(t,x(t))\) the ``metric likelihood'' is defined to be \({\mathcal L}(x)=\inf_{\varepsilon>0}\alpha(\{u'| u'(t)\in F(t,u(t)+\varepsilon B)+\varepsilon B\), \(u(t_ 0)=x_ 0\), \(\| u- x\|<\varepsilon\})\), where \(\alpha\) denotes a measure of non- compactness. It is assumed that \(F\) is a compact valued, upper semicontinuous multifunction. One of the main results is a characterization of solutions of (2) \(x'(t)\in\text{extco}F(t,x(t))\) as those of (1) which have likelihood zero. A generalization of Olech's lemma for differential inclusion (1) is given.