FPRAS for #P-complete problems I just found the following sentence from the #P wiki page:

"Jerrum, Valiant, and Vazirani showed that every #P-complete problem either has an FPRAS, or is essentially impossible to approximate; if there is any polynomial-time algorithm which consistently produces an approximation of a #P-complete problem which is within a polynomial ratio in the size of the input of the exact answer, then that algorithm can be used to construct an FPRAS.[3]"

http://en.wikipedia.org/wiki/Sharp-P-complete

the referece [3] is 
Mark R. Jerrum; Leslie G. Valiant; Vijay V. Vazirani (1986). "Random Generation of Combinatorial Structures from a Uniform Distribution". Theoretical Computer Science (Elsevier) 32: 169–188.

I took a quick look at [3]. But it seems to me that the results of [3] do not contain anything similar to what is in the wiki page. Is there a mistake in the wiki page? Thanks.
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.