Short Note: Every Large Set of Integers Contains a Three Term Arithmetic   Progression
  I show that a trivial modification of a standard proof of the Roth's Theorem on triples in arithmetic progression would lead to the following Theorem: If A is a "large set" that is its elements are monotone increasing integers and the sum of reciprocals of its elements diverges then the sequence contains an arithmetic progression of length three. 
Gabor Korvin
math.NT