Adam Yauch, who has undergone treatment for a cancerous parotid gland and a lymph node, became a vegan at the recommendation of his Tibetan doctors.
He is survived by his wife and daughter. It is not yet known whether his death is related to the disease.
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The £55.7 billion project will “fundamentally” change how Britons view rail travel, the Government-backed firm behind the scheme says.
Judd’s lawyer called Weinstein’s arguments “offensive”.
Mrs May will meet business representatives on the Northern Ireland side of the border on Thursday afternoon.