Milnor Fibrations and the Thom Property for maps $f\bar{g}$

We prove that every map-germ $f\bar{g}:({\text{C}}^n,\text{0})\to (\text{C},0)$ with an isolated critical value at 0 has the Thom $a_{f\bar{g}}$-property. This extends Hironaka’s theorem for holomorphic mappings to the case of map-germs $f\bar{g}$ and it implies that every such map-germ has a Milnor-L^e fibration defined on a Milnor tube. One thus has a locally trivial fibration $\phi: \mathbb S_\e \setminus K \to \mathbb S^1$foreverysufficientlysmallspherearound$\0$, where $K$ is the link of $f\bar{g}$ and in a neighbourhood of $K$ the projection map $\varphi$ is given by $f\bar{g}\mathrm{/}\mathrm{\mid }f\bar{g}\mathrm{\mid }$.