Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.
"Supermartingales as Radon–Nikodym densities and related measure extensions." Ann. Probab. 43 (6) 3133 - 3176, November 2015. https://doi.org/10.1214/14-AOP956