  Spatial constraint systems (scs) are semantic structures for reasoning about
spatial and epistemic information in concurrent systems. We develop the theory
of scs to reason about the distributed information of potentially infinite
groups. We characterize the notion of distributed information of a group of
agents as the infimum of the set of join-preserving functions that represent
the spaces of the agents in the group. We provide an alternative
characterization of this notion as the greatest family of join-preserving
functions that satisfy certain basic properties. For completely distributive
lattices, we establish that distributed information of a group is the greatest
information below all possible combinations of information in the spaces of the
agents in the group that derive a given piece of information. We show
compositionality results for these characterizations and conditions under which
information that can be obtained by an infinite group can also be obtained by a
finite group. Finally, we provide an application on mathematical morphology
where dilations, one of its fundamental operations, define an scs on a powerset
lattice. We show that distributed information represents a particular dilation
in such scs.
