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1. A designation given to a public establishment, such as a school or hospital, that is in need of improvement. Often used in the phrase "in special measures." Primarily heard in UK. My son's school is currently in special measures, so he's transferring to a different one next year.
2. Steps that must be taken, however unusual or extreme, to bring about some outcome. Oh, I will take special measures to ensure that the neighbors' dog stops barking, even if I have to buy him a muzzle myself! Don't worry, we took special measures to make sure that nobody finds us in here—we have furniture blocking all the doors.