A brake system of an elevator, an escalator or a moving walkway includes a brake device with at least one brake shoe. The brake shoe has an effective surface which during brake use is pressed against a friction surface, which is moving or movable relative to the effective surface, of a counter-member. The brake system also includes a feed device which is supplied by a fluid source. A fluid can be fed between the effective surface of the brake shoe and the friction surface, which faces it, by means of the feed device. The friction between the effective surface and the friction surface can be influenced by the feed of the fluid.