  In the paper we are dealing with metric measure spaces of diameter at most
one and of total measure one. Gromov introduced the sampling compactification
of the set of these spaces. He asked whether the metric measure space
invariants extend to the compactification. Using ideas of the newly developed
theory of graph limits we identify the elements of the compactification with
certain geometric objects and show how to extend various invariants to this
space. We will introduce the notion of ultralimit of metric measure spaces,
that will be the main technical tool of our paper.
