  In our previous article with Yukio Kametani, we investigated the geometric
structure underlying a large scale interacting system on infinite graphs, via
constructing a suitable cohomology theory called uniformly local cohomology,
which reflects the geometric property of the microscopic model, using a class
of functions called the uniformly local functions. In this article, we
introduce the co-local functions on the geometric structure associated to a
large scale interacting system. We may similarly define the notion of uniformly
local functions for co-local functions. However, contrary to the functions
appearing in our previous article, the co-local functions reflect the
stochastic property of the model, namely the probability measure on the
configuration space. We then prove a decomposition theorem of Varadhan type for
closed co-local forms. The space of co-local functions and forms contain the
space of $L^2$-functions and forms. In the last section, we state a conjecture
concerning the decomposition theorem for the $L^2$-case.
