Inductive freeness of Ziegler's canonical multiderivations for reflection arrangements

More precisely, let A=A(W) be the reflection arrangement of a complex reflection group W. By work of Terao, each such reflection arrangement is free. Thus so is Ziegler's canonical multiplicity on the restriction A″ of A to a hyperplane. We show that the latter is inductively free as a multiarrangement if and only if A″ itself is inductively free.