  Let A \subseteq [1,..,N]^2 be a set of cardinality at least N^2/(log log
N)^c, where c>0 is an absolute constant. We prove that A contains a triple
{(k,m), (k+d,m), (k,m+d)}, where d>0. This theorem is a two-dimensional
generalization of Szemeredi's theorem on arithmetic progression.
