Treeable Graphings are Local Limits of Finite Graphs

Let G be a graphing, that is a Borel graph defined by d measure preserving involutions. We prove that if G is treeable then it arises as the local limit of some sequence (Gn) of graphs with maximum degree at most d. This extends a result by Elek (for G a treeing) and consequently extends the domain of the graphings for which Aldous–Lyons conjecture is known to be true.