What was found
CABIN PRESSURE INFLOW LOW MESSAGE AT APPROXIMATELY 6000 FT ON CLIMB, CABIN PRESSURE SEEMED NORMAL. CLIMBED TO FL 250, LIMITED DUE TO EXISTING MEL 21-50-01, RELATED TO A RT PACK OVERHEAT. THE CABIN CONTINUED TO CLIMB SO DESCENDED TO FL190. AT FL190 CABIN STABILIZED AT ABOUT 7000 FT. DURING DESCENT INTO LAX THE CABIN DID NOT DESCEND AS RAPIDLY AS IT SHOULD HAVE, AT 5000 FT, CABIN WAS 4400 FT. DECLARED EMERGENCY. THERE WAS NO EXPEDITED DESCENT OR OXYGEN MASK DEPLOYMENT. MAINTENANCE REPLACED THE RT ACM & FLOW CONTROL VALVE. ALSO REPLACED NR 2 CABIN PRESSURE CONTROLLER. SYSTEM CHECKS NORMAL. 14 CFR PART 121.703 DOES NOT DIFFERENTIATE REPORTING CRITERIA IF ATC DECLARES AN EMERGENCY ON BEHALF OF THE FLIGHT CREW.