ACR FLC CONTINUED APCH AFTER POSSIBLY RECEIVING BELOW MINIMUMS WX PRIOR TO THE FINAL APCH SEGMENT.

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CAPT WAS HIGH ON ESTIMATED DSCNT PROFILE COMING INTO LAX. LAX APCH ASKED IF HE WOULD BE ABLE TO GET DOWN OK. I WAS TOLD TO ASK FOR A 360 DEG TURN TO GET DOWN; APCH GAVE US TURNING VECTORS IN LIEU OF A 360 DEG TURN. DURING THE TURN; APCH CLRED US FOR ILS RWY 7L APCH. RVR WAS 1400 FT AND ? AND ? FT. SINCE RWY 7L IS A CAT II APCH ONLY TOUCHDOWN RVR OF 1200 FT RVR IS REQUIRED. DURING APCH; APCH CTLR SAID RVR IS 1000 FT AND ? AND ? FT. ALTHOUGH ONCE ESTABLISHED ON FINAL SEGMENT OF APCH; WE CAN CONTINUE IF RVR DROPS BELOW REQUIRED RVR OF 1200 FT. CAPT ASKED CTLR IF HE WAS SURE RVR WAS 1000 FT AND NOT 1200 FT. APCH REPLIED RVR 1200 FT RVR AND ? AND ? FT. WE CONTINUED AND LANDED. IN RETROSPECT; CAPT COULDN'T BE ABSOLUTELY SURE IF THE CTLR RPTED THE RVR OF 1000 FT AND ? AND ? FT PRIOR TO INTERCEPTING THE FINAL APCH SEGMENT OR ONCE ESTABLISHED ON THE FINAL APCH SEGMENT. THIS COULD AFFECT THE LEGALITY OF THE APCH. ALTHOUGH THE CTLR DID COME BACK WITH CORRECTED RVR OF 1200 FT AND ? AND ? FT. ARRIVING HIGH ON THE APCH PROFILE DIDN'T ALLOW US ENOUGH TIME TO THOROUGHLY DIGEST THE RVR READINGS AS THE FOG ROLLED IN. NEXT TIME I WILL ASK FOR ANOTHER TURN OR A VECTOR UNTIL WE ARE IN AGREEMENT AS TO THE APCH LEGALITY. SUPPLEMENTAL INFO FROM ACN 314300: DURING THE DSCNT AND SUBSEQUENT VECTORING FOR THE APCH INTO LAX; THE VISIBILITY BEGAN TO DETERIORATE DUE TO APCHING FOG BANK FROM THE W. INITIALLY THEY WERE LNDG TO THE E ON RWY 7L AND THAT APCH WAS LOADED AND BRIEFED. ABOUT 20 MI OUT; THE ARPT CHANGED AROUND TO LAND TO THE W. THE VISIBILITY BEGAN TO DEGRADE FURTHER AND RVR WAS RPTED AT 1000 FT AND 800 FT AND 800 FT. WE WERE THEN ASKED IF WE COULD ACCEPT THE APCH. I MISREAD THE RWY 25L APCH TO BE A CAT II/III APCH AND SAID WE COULD ACCEPT THE APCH. AFTER TURNING THE ACFT OVER TO THE FO FOR A MONITORED APCH AND TO COMPLETE THE CAT III BRIEFING; I REALIZED MY MISTAKE; RWY 25L WAS ONLY CAT II; AND ASKED APCH TO VERIFY THE RVR FOR RWY 25L. THEY SAID THE RVR WAS 1400 FT AND 800 FT AND 800 FT WHICH WAS CAT II MINIMUMS SO I CONTINUED THE APCH AND LNDG. I FEEL THAT THE 3 RWY CHANGES ALONG WITH THE 360 DEG VECTORED PATTERN TO GET DOWN TO APCH ALT PLUS BEING ASKED IF WE COULD EXCEPT THE APCH TO A RWY THAT WAS BELOW MINS WERE CONTRIBUTING FACTORS; A LOT HAPPENS IN AN FMS TYPE ACFT AT THE LAST OF A FLT SO ANY ADDED CHANGES BY ATC MAKES FOR ADDED AREAS FOR MISTAKES TO BE MADE. ALL OF THIS HAPPENED AROUND 2500 FT AND I'M NOT EVEN SURE THERE WAS A LEGALITY PROB.