  In this paper, we prove that for $\mathcal{C}^1$ generic volume-preserving
Anosov diffeomorphisms of a compact Riemannian manifold, Liv\v{s}ic measurable
rigidity theorem holds. We also prove that for $\mathcal{C}^1$ generic
volume-preserving Anosov flows of a compact Riemannian manifold, Liv\v{s}ic
measurable rigidity theorem holds.
