The RIAA has asked a New York District Court to shut down the world's most installed file-sharing application, Limewire. The record labels argue that the Gnutella-based download client might have caused billions of dollars in lost revenue and that it's therefore one of the largest threats to the music industry's revenue.

The RIAA and the company behind Limewire have been fighting out a legal dispute since 2006, but in recent weeks the case seems to have been moving along faster than ever before.

Last month, a US Court ruled that the Lime Group, the company behind Limewire, was liable for the copyright infringements committed by its users. Two weeks later the Lime Group asked the court to reconsider this judgment. This request was followed by one from the RIAA, asking the court to shut down Limewire via a permanent injunction.

The RIAA argues that Limewire’s operation has to be stopped immediately, to avoid it doing any more harm to the music industry in the future. Interestingly enough, very little argumentation or evidence is given for any real losses suffered by the record labels.

“It is patently obvious that the rampant illegal conduct that Lime Wire intentionally induced, and for which it has been adjudged liable, will continue uninterrupted day after day unless and until the Court issues an injunction to rein in this massive infringing operation,” RIAA’s lawyers wrote to the Court.

“Every day that Lime Wire’s conduct continues unabated guarantees harm to Plaintiffs that money damages cannot and will not compensate,” RIAA’s legal team continues. “The scope of the infringements that Lime Wire induced – and that continue to this day – boggles the mind.

The RIAA is right in saying that Limewire users have committed, and are committing many millions of infringements, but there is very little evidence for the massive damage that this has cost. Thus far, a real assessment of the claimed losses has been lacking in most file-sharing related legal cases.

“It does not require sophisticated mathematics to calculate that the likely damage award in this case will run into the hundreds of millions, if not the billions of dollars,” the RIAA argues. However, one of the few academic papers (pdf) that looked at the relationship between actual downloads and lost sales to the music industry has found that there’s no direct correlation.

With that said, the outcome of this case could potentially change the file-sharing landscape for good. Despite BitTorrent being the leading file-sharing protocol for several years already, Limewire is most likely the most installed P2P application on the market. In 2008 LimeWire was the most installed P2P application with an impressive market-share of 37%, compared to 14% for runner-up uTorrent.

If the RIAA score a victory in court against Limewire, hundreds or millions of people will have to seek an alternative download client, which might mean a significant boost in user numbers for some of the major BitTorrent applications.