We report a measurement of the inclusive muon and b-quark production cross sections in pp¯ collisions at s=1.8 TeV using the D0 detector at the Fermilab Tevatron collider. The inclusive muon spectrum extends over the kinematic range |yμ|<0.8 and 3.5<pTμ<60GeV/c, and is well described by the expected contributions from various known sources. The b-quark production cross section for |yb|<1.0 and pTb>6GeV/c is extracted, and agrees with next-to-leading order QCD predictions within the experimental and theoretical uncertainties.Received 12 December 1994DOI:https://doi.org/10.1103/PhysRevLett.74.3548©1995 American Physical Society