  We introduce the concept of quotient-convergence for sequences of submodular
set functions, providing, among others, a new framework for the study of
convergence of matroids through their rank functions. Extending the limit
theory of bounded degree graphs, which analyzes graph sequences via
neighborhood sampling, we address the challenge posed by the absence of a
neighborhood concept in matroids. We show that any bounded set function can be
approximated by a sequence of finite set functions that quotient-converges to
it. In addition, we explicitly construct such sequences for increasing,
submodular, and upper continuous set functions, and prove the completeness of
the space under quotient-convergence.
