A coupling method is used to give another proof of Blackwell's renewal theorem. The nature of the proof is probabilistic, using in an essential way the nonlattice property of the lifetime distribution and the Hewitt-Savage zero-one law.
"A Probabilistic Proof of Blackwell's Renewal Theorem." Ann. Probab. 5 (3) 482 - 485, June, 1977. https://doi.org/10.1214/aop/1176995810