We give a mathematical definition of stationary, asymptotically memoryless, continuous-time channels, and prove a coding theorem and its converse for such channels.
T. T. Kadota. A. D. Wyner. "Coding Theorem for Stationary, Asymptotically Memoryless, Continuous-time Channels." Ann. Math. Statist. 43 (5) 1603 - 1611, October, 1972. https://doi.org/10.1214/aoms/1177692392