Removal lemma for infinitely-many forbidden hypergraphs and property   testing
  We give an extension of a graph result by Alon and Shapira. And it affirmatively settles a question on property testing raised by them. All monotone hypergraph properties and all hereditary partite hypergraph properties are testable. Our proof is constructive and based on a new hypergraph regularity lemma. 
Yoshiyasu Ishigami