I mean a theorem of the following kind. Let $A$ be a C*-algebra, and let $\pi: A\to B(H)$ be its representation. Then there exist a set $P$ with a positive measure $\mu$, a field of Hilbert spaces such that $H\simeq \int_P H_p d\mu(p)$, and irreducible representations $\pi_p: A\to B(H_p)$ such that $\pi=\int_P \pi_p d\mu(p)$.

In classical references (Dixmier/Takesaki/Kadison...) both $A$ and $H$ are assumed to be separable. Is there a canonical reference for the nonseparable case?

I have found two articles, not counting particular cases: S. Teleman On reduction theory. {\it Rev. Roumaine Math. Pures Appl.} {\bf 21}, no.~4 (1976), 465--486. and R. Henrichs Decomposition of invariant states and nonseparable C*-algebras. Publ. Res. Inst. Math. Sci. 18, 159-181 (1982). Both use definition of fields of Hilbert spaces given by W. Wils in Direct integrals of Hilbert spaces I. {\it Math. Scand.} {\bf 26} (1970), 73--88.

Both prove the theorem above (Henrichs for the unital case), with one main difference: in Teleman's version, $P$ is a subset of pure states of $A$, but $\mu$ may not be regular (not every set is approximated by compacts from inside). In Henrichs', $\mu$ is regular but one and the same irrep can repeat, even for every $p$.

In the history of this question there were lots or erroneous articles, so I treat these two also with caution. I've gone through Teleman's proof(because it is self-contained). It seems correct, but it turns out that $\pi_p$ may be zero, and this is not indicated in the paper. Through Henrichs I didn't go in detail. He relies on a rarely used theorem of Tomita, for which he however gives an independent proof.

So this is my question: do you use this theory, and if yes, what authors do you refer to?