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

Liv\v{s}ic Measurable Rigidity Theorem for \mathcal{C}^1 Generic Volume-preserving Systems