We investigate the existence of an absolutely continuous martingale measure. For continuous processes we show that the absence of arbitrage for general admissible integrands implies the existence of an absolutely continuous (not necessarily equivalent) local martingale measure. We also rephrase Radon-Nikodym theorems for predictable processes.
"The Existence of Absolutely Continuous Local Martingale Measures." Ann. Appl. Probab. 5 (4) 926 - 945, November, 1995. https://doi.org/10.1214/aoap/1177004600