A measurement of inclusive semileptonic branching fractions of b hadrons produced in Z0 decays is presented. An enriched Z0→bb¯ sample is obtained with a lifetime flavour-tagging technique. The leptonic events are then selected from this sample, and classified according to their origin, which is determined by comparing the distribution of several kinematic variables using artificial neural network techniques. Using 3.6 million multihadronic events collected with the OPAL detector at energies near the Z0 resonance, the values
BR(b → ℓX) = (10.84 ± 0.09 (stat.) ± 0.21 (syst.) +0.21−0.13 (model))
BR(b → c → ℓX) = ( 8.39 ± 0.15 (stat.) ± 0.22 (syst.) +0.33−0.29 (model)).
are measured, where b denotes all weakly decaying b hadrons and ℓ represents either e or μ. The second error includes all experimental systematic uncertainties whereas the last error is due to uncertainties in modelling of the lepton momentum spectrum in semileptonic decays and b quark fragmentation. The average fraction of the beam energy carried by the weakly decaying b hadron, ⟨xE⟩, is measured to be
(xE) = 0.709 ± 0.003 (stat.) ± 0.003 (syst.) ± 0.013 (model)
where the modelling error is dominated by the choice of b fragmentation model. The agreement between data and various semileptonic decay models and fragmentation functions is also investigated.