i thought i would be able to sleep behind one of the gate counters in the AA terminal, but around midnight (IIRC) security did a sweep of the entire terminal and herded me down to baggage claim. there were a couple of people sleeping on the ground, but there's nowhere else to sleep. i tried to sleep sitting up in a chair, but it was miserable. you also have the noise of the passing cars and the opening doors. not to be forgotten is the lingering fear that a passerby is going to enter the baggage area and rob/kill you. i don't mind sleeping in a secured area, but the baggage area at LAX is nightmarish.