On the Multiplicity of a C ..differentiable Function.germ

Risler & Trotman in 1997 proved that the multiplicity of an analytic function germ is left.right lipschitz invariant, which provided a partial answer to Zariski conjecture. In this note, based on the recent work of Comte, Milman & Trotman, we generalize the work of them to prove that the multiplicity of a C ..differentiable function germ is also left.right lipschitz invariant.