This was a generalization referring to the part of the world that they were interested in. AT: "all over the inhabited world" or "throughout the Roman Empire" (See: [[rc://en/ta/man/translate/figs-hyperbole]])
Luke's audience would know that Claudius was the emperor of Rome at that time. AT: "when Claudius was the Roman emperor" (See: [[rc://en/ta/man/translate/figs-explicit]] and [[rc://en/ta/man/translate/translate-names]])