We characterize the sequences {nj} of integers for which, for every finite continuous Borel measure μ on [0, 1], the Cesàro averages of the sequence \(\{\hat{\mu}(n_{j})\}\) converge to 0 (where \(\hat{\mu}(n)=\int_{0}^{1}\text{exp}(-2\pi inx)\mathrm{d}\mu(x) \) stands for the n-th Fourier–Stieltjes coefficient of μ). Some relevant problems on distribution modulo 1 of real sequences are studied. The slow convergence of functions is introduced and used as a tool. The proof of the equivalence of several definitions of slow convergence utilizes H. P. Rosenthal’s combinatorial result.
