  Let M be an n-manifold, and let A be a space with a partial sum behaving as
an n-fold loop sum. We define the space C(M;A) of configurations in M with
summable labels in A via operad theory. Some examples are symmetric products,
labelled configuration spaces, and spaces of rational curves.
  We show that C(I^n,dI^n;A) is an n-fold delooping of C(I^n;A), and for n=1 it
is the classifying space by Stasheff. If M is compact, parallelizable, and A is
path connected, then C(M;A) is homotopic to the mapping space
Map(M,C(I^n,dI^n;A)).
