A membrane filter for filtering a liquid to be filtered, the membrane filter including at least one membrane carrier to which membranes are fixed, the membranes allowing a liquid permeate to be filtered out of the liquid, and the membrane carrier includes a permeate collecting chamber to which the membranes are connected in an open manner on the permeate side, and also comprises a permeate outlet for the discharge of the permeate out of the permeate collecting chamber; a gas distribution system which is arranged below the at least one membrane carrier and which has at least one downwardly open and upwardly closed tub which has a wall with downwardly open vertical slots for the distribution of a gas into the liquid to be filtered, at least one gas inlet leading into the gas distribution system. The invention also relates to a method for filtering a liquid.