We have studied J/psi production in p (p) over bar collisions at root
s = 1.8 TeV with the DO detector at Fermilab using mu(+)mu(-) data. We
have measured the inclusive J/psi production cross section as a funct
ion of J/psi transverse momentum, p(T). For the kinematic range p(T) >
8 GeV/c and \eta\ < 0.6 we obtain sigma(p (p) over bar --> J/psi + X)
. Br(J/psi --> mu(+)mu(-)) = 2.08 +/- 0.17(stat) +/- 0.46(syst) nb. U
sing the muon impact parameter we have estimated the fraction of J/psi
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. Fr
om the information on the event topology the fraction of nonisolated J
/psi events has been measured to be f(nonisol) = 0.64 +/- 0.08(stat) /- 0.06(syst). We have also obtained the fraction of J/psi events resu
lting from radiative decays of chi(c) states, f(chi) = 0.32 +/- 0.07(s
tat) +/- 0.07(syst). We discuss the implications of our measurements f
or charmonium production processes.