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Microsoft and three of its key mobile partners — HTC, Nokia and Sony Ericsson — filed a challenge in Europe today seeking to invalidate Apple’s trademarks on the phrases “App Store” and “Appstore.” It’s the latest move in a struggle over rights to a phrase at the center of the booming mobile economy.

The Redmond company and its partners argue in the European filings that the trademarks shouldn’t have been granted to Apple because they lack distinctiveness.

Amazon, which was sued by Apple in the U.S. over the name of its Android “Appstore,” filed a similar action in Europe last month.

Microsoft is also challenging Apple’s claim over “App Store,” in the U.S., seeking to block its registration of the trademark — saying it’s too generic to warrant intellectual property protection.

Apple has argued that the public associates “App Store” with its own mobile marketplace, and that many of its competitors have had no problem finding alternative terms — including Microsoft with its own Windows Phone Marketplace.

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