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The mass of a protostar is calculated from the infall and dispersal of a dense core in a molecular cloud. An isothermal sphere in a uniform background collapses, while outflows disperse the available gas over a time scale t_d. The protostar mass approaches a time-independent value if t_d is comparable to the core free-fall time t_core, and if the core has enough density contrast over its background. The final protostar mass is approximately the initial gas mass whose free-fall time equals t_d. This mass matches the peak of the IMF for gas temperature 10 K, peak and background densities 10^6 and 10^3 cm-3, and time scale ratio t_d/t_core=0.6. The accretion luminosity exceeds 1 L_O for 0.1 Myr, similar to the duration of the "Class 0" phase. For t_d/t_core=0.4-0.8 and temperature 7-50 K, protostar masses range from brown dwarfs, 0.08 M_O, to massive stars, 5 M_O. Over this range, protostar and core masses correlate, with mass ratio 0.2-0.6, as expected if the core mass distribution has the same shape as the IMF.
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