  Borgs, Chayes, Cohn and Holden (2016+) recently extended the definition of
graphons from probability spaces to arbitrary $\sigma$-finite measure spaces,
in order to study limits of sparse graphs. They also extended the definition of
the cut metric, and proved various results on the resulting metric space.
  We continue this line of research and give various further results on
graphons and the cut metric in this general setting, extending known results
for the standard case of graphons on probability spaces. In particular, we
characterize pairs of equivalent graphons, and we give new results on
completeness and compactness.
