  The possibility of the first measurement of Bjorken unpolarized sum rule for
$F_1$ structure function of $\nu N$ deep-inelastic scattering at Neutrino
Factories is commented. The brief summary of various theoretical contributions
to this sum rule is given. Using the next-to-leading set of parton
distributions functions, we simulate the expected $Q^2$-behavior and emphasize
that its measurement can allow to determine the value of the QCD strong
coupling constant $\alpha_s$ with reasonable theoretical uncertainty, dominated
by the ambiguity in the existing estimates of the twist-4 non-perturbative
$1/Q^2$-effect.
