FAIR TERRITORY is that part of the playing field within, and including the first base and third base lines, from home base to the bottom of the playing field fence and perpendicularly upwards. All foul lines are in fair territory.
Lines on a baseball field are generally within the area being defined. For instance, a foul line separates fair territory from foul territory and is part of fair territory, and the lines of the batter's box are within the batter's box [Rule 6.03].
Ball hits yellow line. Yellow line is part of fence and separates live ball territory from dead ball territory. The ball is live and in play.
Since the definition of fair territory extends perpendicularly, it is not necessary for a fielder to be touching fair territory to cause a ball to be fair. In other words, it is the position of the ball and not the player that matters for a fair/foul call.
First baseman lets ball roll fair before picking it up while standing in foul territory. Fair ball.
Rule 2.00 FAIR BALL
Rule 2.00 FOUL BALL
Rule 2.00 INTERFERENCE
Rule 4.05 CMT