A CARJ CREW; LOW ON FUEL; LANDED AT PNS WITH WX BELOW MINIMUMS.

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AFTER BEING ON DUTY SINCE XA05 AM IN THE MORNING; WE DEPARTED FOR GPT AT XN15. AT THE TIME OF DEP; THE WX AT GPT WAS ABOVE AND FORECAST TO BE ABOVE LNDG MINIMUMS. WHEN WE ARRIVED IN THE GPT AREA THE WX WAS BELOW LNDG MINIMUMS; DISPATCHER AND I AGREED TO DIVERT TO PNS; PENSACOLA. AN ALTERNATE ARPT WAS REQUIRED ON OUR RELEASE; SO FUEL WAS NOT TOO BIG A PROB CONSIDERING THAT THE WX IN PNS WAS 4 MI VISIBILITY AT THE TIME OF OUR DIVERT. 30 MI OUT OF PNS; THE VISIBILITY DROPPED TO 3/4 OF A MI; WE WERE PLANNING ON THE ILS TO RWY 17; WHICH REQUIRE 1/2 MI OR 2400 FT RVR. WHILE GETTING VECTORED ONTO THE FINAL APCH COURSE AND JUST OUTSIDE THE FAF; THE TWR CTLR RPTED THE RVR AS 2000 FT TOUCHDOWN ZONE AND 5000 FT ROLLOUT. AT THE TIME WE WERE NOW LOW ON FUEL AND VERY FATIGUED DUE TO THE LONG DUTY DAY. I COULDN'T REMEMBER IF WE NEEDED BOTH RVR'S TO BE ABOVE 2400 FT. WITH LOW FUEL AND THE RWY IN SIGHT; INCLUDING THE TOUCHDOWN ZONE LIGHTING AND MARKING; I ELECTED TO LAND. PRIOR TO THE LNDG; WHILE INSIDE THE FINAL APCH FIX; THE TWR CTLR CALLED THE TOUCHDOWN ZONE RVR AT 1800 FT AND THE ROLLOUT RVR AT 2000 FT. UNDER THE FATIGUE; MY DECISION TO CONTINUE THE APCH I QUESTION. HAVE YET TO DETERMINE IF WE VIOLATED FAR'S BY INITIATING THE APCH.