We report measurements of the transition frequencies 4s S-2(1/2)-4p P-2(1/2) and 4s S-2(1/2)-4p P-2(3/2) of the potassium isotopes 39, 40, and 41 through an atomic beam experiment with a fractional uncertainty of about 2x10(-10). For frequency calibration, a fs-laser comb referenced to a Cs atomic clock was used. Compared to previous results, hyperfine constants for the states 4p P-2(1/2) and 4p P-2(3/2) and isotope shifts are given with a considerably reduced uncertainty. This paper also resolves the discrepancy of transition frequencies measured by Banerjee [Phys. Rev. A 70, 052505 (2004)] and Scherf [Z. Phys. D 36, 31 (1996)] and the hyperfine constant A(K-39,P-2(1/2)) reported by Banerjee et al.
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