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In the preceeding article, we have generalized to the twisted case theproposition 3.1 of the third Arthur's article on the stabilization of the traceformula. The base-field was p-adic. Here, we prove the same result over thereal base-field. We prove also auxiliary results on the differential equationsand the jump's conditions satisfied by the weighted orbital integrals.

Stabilisation de la formule des traces tordue IX : propri\'et\'es des int\'egrales orbitales pond\'er\'ees $\omega$ equivariantessurlecorpsr\'eel