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The authors have studied J/{psi} production in p{anti p} collisions at {radical}s = 1.8 TeV with the D0 detector at Fermilab, using a {mu}{sup +}{mu}{sup {minus}} data sample corresponding to an integrated luminosity of 13 pb{sup {minus}1}. They have measured the inclusive J/{psi} production cross section as a function of J/{psi} transverse momentum p{sub T}. For the kinematic range p{sub T} > 8 GeV/c and {vert_bar}{eta}{vert_bar} < 0.6 they obtain Br(J/{psi} {yields} {mu}{sup +}{mu}{sup {minus}}) {center_dot} {sigma}(p{anti p} {yields} J/{psi} + X) = 1.93 {+-} 0.16(stat) {+-} 0.43(syst) nb. Using the muon impact parameter they have estimated the fraction of J/{psi} mesons coming from B meson decays to be f{sub b} = 0.35 {+-} 0.09 (stat) {+-} 0.10 (syst) and inferred the inclusive b production cross section. From the information on the event topology a fraction of non-isolated J/{psi} events has been measured to be f{sub non-isol} = 0.64 {+-} 0.09(stat) {+-} 0.06(syst). They have also obtained the fraction of events resulting from radiative decays of {chi}{sub c} states as f{sub {chi}} = 0.30 {+-} 0.07(stat) {+-} 0.07(syst). They discuss the implications of the measurements for charmonium production processes