Spin asymmetries $A_1$ and structure functions $g_1$ of the proton and the deuteron from polarized high energy muon scattering

We present the final results of the spin asymmetries $A_1$ and the spin structure functions $g_1$ of the proton and the deuteron in the kinematic range $0.0008<x<\mathrm{}0.7\mathrm{}$ and $0.2<\mathrm{}{Q}^2<100\mathrm{}{\mathrm{GeV}}^2.$ For the determination of $A_1,$ in addition to the usual method which employs inclusive scattering events and includes a large radiative background at low x, we use a new method which minimizes the radiative background by selecting events with at least one hadron as well as a muon in the final state. We find that this hadron method gives smaller errors for $x<\mathrm{}0.02,$ so it is combined with the usual method to provide the optimal set of results.