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We analyze the self-focusing effect of a relativistic electron or positron beam traversing through a thin slab of plasma in a linearized fluid theory, and show that the effect is very strong. The idea of employing this effect for a plasma lens suggested by Chen is then reviewed. The self-focusing force can be made uniform over the length of the beam by injecting an appropriate precursor. Computer simulations on both thin and thick plasma lenses are presented, which show reasonable agreement with theoretical predictions.