We consider random perturbations of non-singular measur-\ud
able transformations S on [0; 1]. By using the spectral decomposition\ud
theorem of Komornik and Lasota, we prove that the existence of the\ud
invariant densities for random perturbations of S. Moreover the densi-\ud
ties for random perturbations with small noise strongly converges to the\ud
deinsity for Perron-Frobenius operator corresponding to S with respect\ud
to L1([0; 1])-norm
