  The theory of measured quantum groupoids, as defined by Lesieur and myself,
was made to generalize the theory of quantum groups made by Kustarmans and
Vaes, but was only defined in a von Neumann algebra setting; Th. Timmermann
constructed locally compact quantum groupoids, which is a C*-version of quantum
groupoids. Here, we associate to such a locally compact quantum groupoid a
measured quantum groupoid in which it is weakly dense; we then associate to a
measured quantum groupoid a locally compact quantum groupoid which is weakly
dense in the measured quantum groupoid, but such a locally compact quantum
groupoid may be not unique; we construct a duality of locally compact quantum
groupoids. We give then examples of locally compact quantum groupoids.
