Products of quasi-measures

A quasi-state is a positive functional on $C(X)$ that is only assumed to be linear on singly-generated subalgebras. We consider the ``iterated integral'' of two quasi-states and determine when this gives a quasi-state on the product space. We also provide explicit formulas for the corresponding quasi-measures in case it does. Finally, we show the general failure of Fubini's Theorem for quasi-states.