ON THE CONTINUITY OF THE TIME CONSTANT OF FIRST-PASSAGE PERCOLATION.

Let U be the distribution function of the non-negative passage time of an individual edge of the square lattice, and let a//o//n be the minimal passage time from (0,0) to (n,0). The process a//o//n/n converges in probability as n approaches infinity to a finite constant mu (U) called the time constant. It is proved that mu (U//k)approaches mu (U) whenever U//k converges weakly to U.