  It is proved that for any domain in $\mathbb C^n$ the Caratheodory--Eisenman
volume is comparable with the volume of the indicatrix of the Caratheodory
metric up to small/large constants depending only on $n.$ Then the
"multidimensional Suita conjecture" theorem of Blocki and Zwonek implies a
comparable relationship between these volumes and the Bergman kernel.
