The Annals of Probability

Supermartingales as Radon–Nikodym densities and related measure extensions

Nicolas Perkowski and Johannes Ruf

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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.

Article information

Ann. Probab., Volume 43, Number 6 (2015), 3133-3176.

Received: September 2013
Revised: July 2014
First available in Project Euclid: 11 December 2015

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Zentralblatt MATH identifier

Primary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx} 60G44: Martingales with continuous parameter 60H99: None of the above, but in this section

Change of measure finitely additive measure Föllmer measure supermartingale Fatou convergence Caratheodory Radon–Nikodym


Perkowski, Nicolas; Ruf, Johannes. Supermartingales as Radon–Nikodym densities and related measure extensions. Ann. Probab. 43 (2015), no. 6, 3133--3176. doi:10.1214/14-AOP956.

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