A Glivenko-Cantelli Theorem for almost additive functions
  We develop a Glivenko--Cantelli theory for monotone, almost additive functions of i.\,i.\,d.\ sequences of random variables indexed by~$\Z^d$. Under certain conditions on the random sequence, short range correlations are allowed as well. We have an explicit error estimate, consisting of a probabilistic and a geometric part. We apply the results to yield uniform convergence for several quantities arising naturally in statistical physics. 
Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselic
math.PR math.ST stat.TH