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Layer resolved Ag(111) surface states corresponding to islands of different thicknesses for ultrathin Ag films on graphite have been observed simultaneously by angle-resolved ultraviolet photoemission. For island thicknesses inferior to the decay length of the surface state wave function the surface state shifts towards higher binding energies. Assuming a simple exponential behaviour of the envelope function a least squares analysis of these experimental results yields a decay length of the surface state wave function of 2.6 ± 0.1 monolayers (6.1 ± 0.2 .