In the Greek text, reference is made to the entire world as opposed to the Roman world. Such a phrase was often used in ancient literature with reference to the inhabited world as known by those writing at the time. In this case it could be a reference to the Roman Empire or to regions within it.1
28 And one of them named Agabus stood up and foretold by the Spirit that there would be a great famine over all the world (this took place in the days of Claudius).