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We demonstrate that the factorization of the tunneling transmission into the product of two surface transmission functions and a vacuum decay factor allows one to generalize Jullière's formula and explain the meaning of the "tunneling density of states" in some limiting cases. Using this factorization we calculate spin-dependent tunneling from clean and oxidized fcc Co surfaces through vacuum into Al using the principal-layer Green's-function approach. We demonstrate that a monolayer of oxygen on the Co(111) surface creates a spin-filter effect due to the Co-O bonding which produces an additional tunneling barrier in the minority-spin channel. This changes the minority-spin dominated conductance for the clean Co surface into a majority-spin dominated conductance for the oxidized Co surface.