Europe stocks down, euro holds near lows after inflation data

* Data seen cementing case for ECB to ease policy * Asian shares rise as U.S., China activity picks up (Updates after inflation data) LONDON, June 3 (Reuters) - European shares dipped on Tuesday and the euro held near 3 1/2-month lows against the dollar after a fall in euro zone inflation cemented the case for the European Central Bank to ease monetary policy later this week. The ECB, which targets inflation of close to 2 percent, meets on Thursday and is widely expected to cut interest rates, including lowering the rate that banks are charged for depositing funds with the central bank to below zero.

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