  When $X$ is locally compact, a quasi-integral (also called a quasi-linear
functional) on $ C_c(X)$ is a homogeneous, positive functional that is only
assumed to be linear on singly-generated subalgebras. We study simple and
almost simple quasi-integrals, i.e., quasi-integrals whose corresponding
compact-finite topological measures assume exactly two values. We present a
criterion for repeated quasi-integration (i.e., iterated integration with
respect to topological measures) to yield a quasi-linear functional. We find a
criterion for a double quasi-integral to be simple. We describe how a product
of topological measures acts on open and compact sets. We show that different
orders of integration in repeated quasi-integrals give the same quasi-integral
if and only if the corresponding topological measures are both measures or one
of the corresponding topological measures is a positive scalar multiple of a
point mass.
