Parameter testing studies which quantities can be approximated using randomized constant query complexity algorithms. In the case of bounded degree graphs, this is intimately connected with the notion of Benjamini-Schramm convergence.

Gabor Elek observed that measurable graphs arise naturally as limit objects for Benjamini-Schramm convergent graphs sequences. I will describe a general pull-back method that uses this connection to translate results in measure theory to a combinatorial setting. It can be applied to give simple proofs of testability for various graph parameters, as well as to prove a regularity-lemma like decomposition theorem for bounded degree graphs.