Equivalent (true) Martingale Measures and no-arbitrage conditions

I hope this is the correct site for this question, as it is rather theoretical...

In their famous paper, Delbaen and Schachermayer proved that the No Free Lunch with Vanishing Risk condition is equivalent to the existence of the Equivalent Local Martingale Measure. Are there any stronger no-arbitrage type conditions that guarantee that this measure is a true martingale measure (i.e. that all discounted asset prices are true martingales as opposed to merely local ones)?

I would be grateful for (academic) references.

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(If I remember well,) the local nature of the equivalent measure in the NFLVR theory comes from the fact that the market $S$ is a locally bounded semi-martingale. If it is bounded, you obtain an equivalent martingale measure.

Should be in A general version of the fundamental theorem of asset pricing, by Freddy Delbaen and Walter Schachermayer (thanks to Richard's remark, your answer seem to be theorem 1.1 of the paper).

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You can take the paper from here taken from Prof.Schachermayer's homepage –  Richard Aug 18 '12 at 19:47

Their definition of arbitrage is not what a trader would call arbitrage. See http://kalx.net/ftapd.pdf for the details.

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Would you like to go more into detail here? The link is great but having more details in the answer itself would be helpful. –  Richard Dec 2 '14 at 9:55
Quant: Hi, Mr. Trader. I have an arbitrage for you! –  Keith A. Lewis Dec 3 '14 at 12:39
Trader: Great. How much do I make up front? Quant: Nothing. Trader: Okay. How much do I make on the back end? Quant: A positive non-zero amount of money. Trader: Um, how positive are we talking here? Quant: I can't tell you that. Trader: What are the odds I make this positive non-zero amount? Quant: I can't tell you that. Trader: Well, when do I make it? Quant: I can't tell you that. Trader: You call that an arbitrage? Quant: Yes. It is the mathematical definition! Trader: Get the !@#\$%^&* off my trading floor. –  Keith A. Lewis Dec 3 '14 at 12:50
This is a nice joke. But sometimes you can construct (more or less) realistic arbitrage as an example. Maybe in this setting too? If not then we can call it purely mathematical ... –  Richard Dec 3 '14 at 12:54
See kalx.net/fms/fms.html for my latest thinking. It is mathematical folly to waste time proving the hard direction of the FTAP. –  Keith A. Lewis Dec 3 '14 at 12:58