From the abstract: “Let \(\phi^t\) be a topologically mixing Anosov flow on a 3-dimensional compact manifold \(M\). Every unstable fiber (horocycle) of such a flow is dense in \(M\). Sinai proved in 1992 that the one-dimensional SBR measures on long segments of unstable fibers converge uniformly to the SBR measure of the flow. We establish an explicit bound on the rate of convergence in terms of integrals of Hölder continuous functions on \(M\)”.