Geodesic
A~Note on Martingale Measures with Bounded Densities
Informatics and Automation, Stochastic financial mathematics, Tome 237 (2002), pp. 212-216.

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Let $S$ be a discrete-time martingale with a finite horizon. We show that the set of equivalent martingale measures with bounded densities is dense in the set of equivalent martingale measures with respect to the total variation norm. 
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M. Rásonyi. A~Note on Martingale Measures with Bounded Densities. Informatics and Automation, Stochastic financial mathematics, Tome 237 (2002), pp. 212-216. http://geodesic.mathdoc.fr/item/TRSPY_2002_237_a10/

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