  Mimicking the von Neumann version of Kustermans and Vaes' locally compact
quantum groups, Franck Lesieur had introduced a notion of measured quantum
groupoid, in the setting of von Neumann algebras. In this article, we suppose
that the basis of the measured quantum groupoid is central; in that case, we
prove that a specific sub-${\bf C}^*$ algebra is invariant under all the data
of the measured quantum groupoid; moreover, this sub-${\bf C}^*$-algebra is a
continuous field of ${\bf C}^*$-algebras; when the basis is central in both the
measured quantum groupoid and its dual, we get that the measured quantum
groupoid is a continuous field of locally compact quantum groups. On the other
hand, using this sub-${\bf C}^*$-algebra, we prove that any abelian measured
quantum groupoid comes from a locally compact groupoid.
