Logan Paul says he and his brother are taking no chances after Floyd Mayweather's "I'll kill you" threat ... telling TMZ Sports they now have security watching them "at all times."
Floyd dropped the menacing warning to Jake Paul after the younger Paul bro famously stole the boxer's hat during a confrontation at the Logan-Mayweather pre-fight news conference in Miami last week.
Most considered it an empty threat -- after all, nobody really thinks Floyd's going to commit murder over a baseball cap -- but Logan tells us he's taking absolutely no chances.