The actual reason why Carmelo wears an arm sleve is not because of him wanting to be like LeBron. It is because Carmelo has a tatoo some how rperesenting The street gang known as "The Crips", which the NBA diss-allows NBA players to reveal.
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Basketball players wear sleeves on the arm they shoot with so it stays warm. In addition it is an extension of the wrist sweat bands from the old days, keeping the sweat from running down their arm and onto their shooting hand. Keeping their shooting hand dry is important for feel on the ball when passing, dribbling and shooting.
It's a shooting sleeve, a lot of players wear them.
Fun Fact: Ray Allen (Boston Celtics) wears a shooting sleeve on one arm during the regular season and a sleeve on both arms in the playoffs.
He wears an armband so that sweat dripping from his shoulder and upper arm doesn't get on his hand and make it slipery.
Kobe Wears that sleeve to keep his shooting arm warm helps to keep your arms form getting sore are tense.