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It is shown that the Carath\'eodory distance and the Lempert function arealmost the same on any strongly pseudoconvex domain in $\C^n;$ in addition, ifthe boundary is $C^{2+\eps}$-smooth, then $\sqrt{n+1}$ times one of them almostcoincides with the Bergman distance.

Comparison of invariant functions on strongly pseudoconvex domains