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An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(ℝ). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic plane minus an explicit singular set. Finally, via an averaging argument, a geodesic flow-invariant distribution on a closed hyperbolic surface is obtained.