Geodesic
A~Note on Martingale Measures with Bounded Densities
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
@article{TM_2002_237_a10,
     author = {M. R\'asonyi},
     title = {A~Note on {Martingale} {Measures} with {Bounded} {Densities}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {212--216},
     publisher = {mathdoc},
     volume = {237},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_237_a10/}
}
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M. Rásonyi. A~Note on Martingale Measures with Bounded Densities. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 212-216. http://geodesic.mathdoc.fr/item/TM_2002_237_a10/