Media lawyer Paul Gilbert has told Daybreak that judges will have to decide on "whether or not a tweet itself is more than shocking or offensive."
He added: "It's finding a balance between what the law says about this and the freedom of speech."
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On Monday afternoon, numerous Facebook posts claimed a silver Mini had been stolen from the town with a girl in it.
Top temperatures 10 Celsius (50F).
Britain and the European Commission reached agreement on a transition deal which will allow talks on the future trade relationship.