That result meant they have won 13 out of 14 matches so far this season, the best ever start by anyone to a league game.
Barcelona are now six points clear of Atletico Madrid and 11 from champions Real Madrid.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.