Hear the word “jujube,” and your thoughts might turn to the classic candy. But over the next several weeks at your local farmers markets, you’ll probably spot mounds of fresh fruit by the same name.

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Jujube fruit is a sweet, low-calorie fruit high in fiber and antioxidants. Eating jujube may help with digestion and improve sleep. Dried jujube has more sugar, so eat it in moderation. Avoid it if ...