The restriction phenomenon is generally studied in higher dimensions. It refers to the ability of an \(L^p\) function to have its Fourier transform meaningfully restricted to certain hypersurfaces or other subsets \(S\) of \(R^n\) for certain \(p>1\), even though the Fourier transform is not continuous or even pointwise defined. In this paper the author shows that this phenomenon occurs in one dimension as well, when \(S\) is a Salem set - a set whose Fourier dimension and Hausdorff dimension agree. (A set \(S\) is said to have Fourier dimension at least \(\alpha\) if it supports a probability measure whose Fourier transform decays like \(|\xi|^{-\alpha/2}\)). A quick review of the known theory of Salem sets is given in this nice and short paper. The author proves the natural analogue of the famous Tomas-Stein theorem for Salem sets (or more generally for measures with dimension and Fourier decay estimates), although unlike the situation with hypersurfaces, there is no “Knapp” counterexample and the Tomas-Stein argument does not appear to give sharp results. The author also proves an analogous result for “Bochner-Riesz” type multipliers, whose symbol decays as a certain power of the distance to \(S\).