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Let H be a semisimple weak Hopf algebra,A a left H-module algebra.We prove that the injective dimension of the regular A-module is equal to the one of A as the module over the smash product A#H,and equal to the one of the regular A#H-module.Also,we give a necessary and sufficient condition for A being a Gorenstein algebra,in terms of the fixed subalgebra of A under the action of H on A.