Does anyone know a good reference for a proof of the fact that given a dga $A$, an $A\_\infty$-structure on $HA$ is ''the same'' as coherent choices for all of the higher Massey products of $HA$? More concretely the fact I am looking for is something like the following.


When defining the Massey product $\langle x\_1,\dots, x\_n\rangle$ there are multiple non-canonical choices that need to be made, which in turn give multiple cycles that could be called *the* Massey product of $x\_1,\dots, x\_n$. If $M(x\_1,\dots, x\_n)$ is the set of all possible resulting Massey products of $x\_1,\dots, x\_n$, and $\mu\_n$ is the $n$-th $A\_\infty$ structure map (on $HA$), then $$\mu\_n(x\_1\otimes\cdots\otimes x\_n)\in M(x\_1,\dots, x\_n)$$
for all $n$ and $x\_i$. 



Massey Products vs. $A_\infty$-Structures
When $n=3$, this is in Stasheff's *H-spaces from a homotopy point of view*, Chapter 12. For general $n$, it is in a paper of mine with Lu, Wu, and Zhang, "$A\_\infty$-structures in Ext algebras, J. Pure Appl. Alg. **213** (2009), 2017--2037 (Theorem 3.1 and Corollary A.5).


