We study the weak convergence of some measures related to the renewal theorem, extending a result by Feller and Orey.
"A property of the Fourier transform of probability measures on the real line related to the renewal theorem." Proc. Japan Acad. Ser. A Math. Sci. 88 (9) 152 - 155, November 2012. https://doi.org/10.3792/pjaa.88.152