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Grazing bifurcation may cause chaotic motions of impact oscillators.The dynamics phenomenon can be modelled by a discrete map(called Nordmark map)with a square-root singularity.When the dissipation of the impact oscillators is large,Nordmark map can be viewed as a perturbation of a one-dimensional map with a square-root term.We study the one-dimensional map from the measure theoretic point of view,and prove that the map has an ergodic absolutely continuous invariant probability measure in certain parameter set.Since the supports of the absolutely continuous invariant measures have positive Lebesgue measures,they are relevant to physical observations.