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In this work we construct a unified model of dark energy and dark matter. This is done with the following three elements: a gravitating scalar field, phi with a non-conventional kinetic term, as in the string theory tachyon; an arbitrary potential, V (phi); two measures - a metric measure (root-g) and a non-metric measure (Phi). The model has two interesting features: (i) For potentials which are unstable and would give rise to tachyonic scalar field, this model can stabilize the scalar field. (ii) The form of the dark energy and dark matter that results from this model is fairly insensitive to the exact form of the scalar field potential.