Gov. Arnold Schwarzenegger, a former movie actor, has been trying for years to get tax credits to keep California’s signature industry at home.

He got his wish early Thursday when the Legislature approved tax credits for film and television productions as part of an economic stimulus provision of the new state budget.

The credits — capped at $500 million over five years — are modest compared with those offered by other states. Still, the announcement was welcome news to many in Hollywood who were skeptical that the Legislature would help the entertainment industry given the enormousness of the task of plugging the state’s $42-billion budget gap.

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