New higher precision measurements of the hyperfine Zeeman transitions in the ground state of muonium have been performed with use of the high-stopping-density surface \i + beam at the Clinton P 0 Anderson Meson Physics Facility. The results are Ay = 4 463-302.88(16) kHz (0.036 ppm) and n^/np^ 3.183 3461(11) (0.36 ppm). The current theoretical value of Ay agrees well with experiment within the 0.77-ppm error of Ay t^eor , which is due principally to inaccuracy in evaluation of the nonrecoil radiative correction term. The most precise current value of m n /m e is obtained from our value of \ij\x p ,
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