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The board is scheduled to vote on the measure Sept. 13.

Since Bloomberg proposed the ban in May, opponents including members of the restaurant and soft drink industries as well as libertarians have accused him of attempting to institute a “nanny state” with far-reaching government controls that infringe on individual choice. City officials, meanwhile, argue they are trying to save lives in the face of an epidemic that is killing New Yorkers and costing $4 billion a year.

The portion size restrictions would only apply to food-service businesses regulated by the Health Department, including restaurants, food carts, sports arenas and movie theaters. Grocery stores, drug stores and some convenience stores are regulated by the state and would be unaffected.

Drinks that are more than half milk or 70 percent juice would be exempt, and it wouldn’t apply to lower-calorie drinks like water or diet soda, or to alcoholic beverages.

In a letter released Monday by The New England Journal of Medicine, New York University researchers said the ban could affect nearly two-thirds of drinks bought at the city’s fast-food restaurants, according to a survey of more than 1,600 receipts. On average, sugary-drink buyers could consume 74 calories less per fast-food outing, the letter said.

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