FPRAS for #P-complete problems
Jerrum, Valiant and Vazirani showed that if for a "self-reducible" NP-relation, there exists a polynomial time approximate counter which produces a $1 + O(n^{-\beta})$ approximation for some constant $\beta &gt; 0$, then this counter can be bootstrapped to make an an FPRAS for the counting problem.  As far as I know, all known #P-complete problems do correspond to "self-reducible" NP-relations, and hence the claim on Wikipedia.  However the exact claim that an approximate counter which produces a poly($n$) approximation for a self-reducible NP-relation can be bootstrapped to produce an FPRAS for counting was proved by Jerrum and Sinclair.  The citation I can think of the top of my head is Sinclair, 1993.