Abstract We have studied J ψ production in p p collisions at s = 1.8 TeV with the DØ detector at Fermilab using μ + μ − data. We have measured the inclusive J ψ production cross section as a function of J ψ transverse momentum, p T . For the kinematic range p T > 8 GeV/ c and |η| < 0.6 we obtain σ(p p → J ψ + X) · Br( J ψ → μ +μ −) = 2.08 ± 0.17( stat) ± 0.46(syst) nb. Using the muon impact parameter we have estimated the fraction of J ψ mesons coming from B meson decays to be f b = 0.35 ± 0.09(stat)±0.10(syst) and inferred the inclusive b production cross section. From the information on the event topology the fraction of nonisolated J ψ events has been measured to be f nonisol = 0.64 ± 0.08(stat)±0.06(syst). We have also obtained the fraction of J ψ events resulting from radiative decays of χ c states, f χ = 0.32 ± 0.07(stat)±0.07(syst). We discuss the implications of our measurements for charmonium production processes.