Milnor Fibrations and the Thom Property for maps f g

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We prove that every map-germ f g: (ⁿ,) →(,0) with an isolated critical value at 0 has the Thom af g-property. This extends Hironaka's theorem for holomorphic mappings to the case of map-germs f g and it implies that every such map-germ has a Milnor-Lê fibration defined on a Milnor tube. One thus has a locally trivial fibration ϕ: S K → S¹ for every sufficiently small sphere around, where K is the link of f g and in a neighbourhood of K the projection map ϕ is given by f g / | f g|.