  Pyramids introduced by Gromov are generalized objects of metric spaces with
Borel probability measures. We study non-trivial pyramids, where non-trivial
means that they are not represented as metric measure spaces. In this paper, we
establish general theory of invariants of pyramids and construct several
invariants. Using them, we distinguish concrete pyramids. Furthermore, we study
a space consisting of non-trivial pyramids and prove that the space have
infinite dimension.
