The territory, jurisdiction, or province governed by a beglerbeg in the Ottoman Empire.
From Turkish beylerbeylık, combining beglerbeg with the Turkish suffix -lik (meaning 'the place or state of'). English borrowed this compound directly to name Ottoman administrative divisions.
During the Ottoman Empire's height (1300s-1900s), the empire was divided into these huge regional commands, and European traders and diplomats had to learn Ottoman terminology to do business. That's why English has so many Ottoman administrative terms.
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