  We give a formal proof that the space-time average of the vacuum condensate
of mass dimension two, i.e., the vacuum expectation value of the squared
potential $\mathscr{A}_\mu^2$, is gauge invariant in the weak sense that it is
independent of the gauge-fixing condition adopted in quantizing the Yang-Mills
theory. This is shown at least for the small deformation from the generalized
Lorentz and the modified Maximal Abelian gauge in the naive continuum
formulation neglecting Gribov copies. This suggests that the numerical value of
the condensate could be the same no matter what gauge-fixing conditions for
choosing the representative from the gauge orbit are adopted to measure it.
Finally, we discuss how this argument should be modified when the Gribov copies
exist.
