FLC IS REQUIRED TO USE CAPT'S AUTH TO CONTINUE APCH BELOW MINIMUMS AT KIND.

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FLT WAS SCHEDULED FROM EWR TO MDW AND WAS GIVEN HOLDING AT AN ARR FIX DUE TO LOW VISIBILITY. CONTACT WAS MADE WITH DISPATCH AND ADVISED THEM OF HOLD. ALTERNATE WAS SWITCHED FROM DTW TO IND TO ALLOW LONGER HOLD. IND VISIBILITY WAS 2 1/2 MI. WE WERE WITHIN 5 MIN OF AGREED UPON TIME WITH DISPATCH TO DIVERT TO OUR ALT; WHEN MDW APCH STARTED TO VECTOR US FOR AN ILS APCH. APCH WAS UNSUCCESSFUL DUE TO LOW CEILING AT MDW. AFTER RECONTACTING MDW APCH DURING MISS; WE ASKED FOR VECTORS TO OUR ALTERNATE IND AND ADVISED ATL WE WOULD BE MINIMUM FUEL UPON ARR AT IND. AFTER BEING CLRED ILS APCH BY IND APCH CTL; AND SWITCHING TO TWR; TWR ADVISED THAT RVR WAS 2200 FT. MINIMUM PUBLISHED FOR APCH WAS 2400 FT. WE WERE AT ABOUT THE FINAL FIX; GS WAS CAPTURED TO THE BEST OF MY RECOLLECTION. I ADVISED TWR THAT WE WERE CONTINUING THE APCH. TWR LATER ADVISED THE RVR WAS LOWER (1800-2000 FT). CLR RWY WAS SIGHTED AT ABOUT 500-600 FT AGL. UNSURE OF WHEN IND TWR GAVE INITIAL 2200 FT RVR CALL; BEFORE OR AFTER FINAL FIX. I WAS CONTINUING APCH REGARDLESS; BECAUSE OF FUEL STATUS; AND WE WERE AT OUR ALT. DURING VECTORING BY MDW APCH; I WAS ADVISED OF RVR; NEVER CEILING HT. I SHOULD HAVE INQUIRED OF WHAT CEILING ESTIMATE WAS.