  Graphings serve as limit objects for bounded-degree graphs. We define the
``cycle matroid'' of a graphing as a submodular setfunction, with values in
[0,1], which generalizes (up to normalization) the cycle matroid of finite
graphs. We prove that for a Benjamini--Schramm convergent sequence of graphs,
the total rank, normalized by the number of nodes, converges to the total rank
of the limit graphing.
