In particular, when S is the whole real line we obtain the standard convolution equation. Again when S is the half line (0, co), we obtain the Wiener-Hopf equation. S= [0, 1] is still another of the classical equations, known to aerodynamicists as the "lifting line equation." We will be concerned with the uniqueness question for the equation (1), but in the following special sense: We wish to determine conditions on X and the kernel function K, together with class conditions on K and F, which will insure the uniqueness of the solution of (1) for all (measurable) sets S. For each fixed S, uniqueness is equivalent to the statement: