What is the complexity of counting the number of solutions of a P-Space Complete problem? How about higher complexity classes? I guess it would be called #P-Space but I have found only one article vaguely mentioning it. How about the counting version of EXP-TIME-Complete, NEXP-Complete as well as EXP-SPACE-Complete problems? Is there any previous work that can one cite in regards to this or any type of inclusion or exclusion like Toda's Theorem?
The number of satisfying assignments to a boolean formula equals the number of valid quantifications of the formula.  The inductive proof is quite elegant. So #P = #PSpace.