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Interesting that they even put this number forward as (a) it was pretty obviously going to be dismissed, but more importantly (b) exposes the nonsense maths that is being used in these situations.

There is I think increasing awareness that the RIAA and others are making demands which, let's put it politely, rather distort the real picture. If I were them I certainly wouldn't be doing things like this that bring attention to these numbers with little real benefit.

this story is old, and the case was settled for substantially less than all the money in the world:

"A trial to decide on the eventual amount of damages owed by Limewire to thirteen record labels, including Warner and Sony Music, all of which are represented by the Recording Industry Association of America (RIAA), started early in May and went on until on May 13, 2011, when Gorton agreed to pay the 13 record companies $105 million in an out-of-court settlement. " http://en.wikipedia.org/wiki/LimeWire

This is nothing new, nor does the article add much insight IMO. Every news site that reports this seems to say the same thing, that they are sued for "more money than exists in the world." The world GDP is ~$60T, but GDP is a long shot away from the total amount of money that exists in the world. There could be $600T in the money supply but if nobody spent their money, GDP would be $0.
Or the converse. There could be $6T in the money supply, but circulation is high. Sort of like a self-contained ornamental fountain that can flow more gallons per day/month/year than it has capacity to hold.

The real insidious part of such lofty sums is that they usually are predicated on potential lost earnings (and sometimes punitive damages), which historically is obviously nowhere near the numbers requested.