In act 4, scene 1, Antony and Octavius discuss the men who were involved in the conspiracy to murder Julius Caesar. Specifically, they discuss which of the conspirators they might need to kill in order to consolidate their own power. Antony and Octavius expect to rule Rome between them once they have dispatched the army raised by the conspirators. Octavius also thinks that Lodovico should share power with them, but Antony disagrees. He asks, "Is it fit, / The threefold world divided, he should stand / One of the three to share it?"
Antony's question is a rhetorical question, meaning that he does not ask it because he is interested in Octavius' answer but rather to make his own point. Indeed, every rhetorical question has an implied answer, and the implied answer to Anthony's question is that it is not fit, or appropriate, for Lodovico to share power with Antony and Octavius. Antony thinks that Lodovico is too weak. When Antony talks about the "threefold world," he is talking about Rome. As far as Antony is concerned, Rome is the whole world, and he does not want to give a third of it to Lodovico.
Antony's ambitions here later prove to be his undoing. Octavius sees in this scene how Antony speaks ill of his friend behind his friend's back, and he also sees how greedy and ambitious Antony is for power. Later Octavius decides not to share power with Antony but to rule by himself.