# logarithmically convex set

Suppose $G\subset{\mathbb{C}}^{n}$, then we define

 $\log\lVert G\rVert:=\{(\log\lvert z_{1}\rvert,\ldots,\log\lvert z_{n}\rvert)% \in{\mathbb{R}}^{n}\mid(z_{1},\ldots,z_{n})\in G\}.$
###### Definition.

We say $G\subset{\mathbb{C}}^{n}$ is a logarithmically convex set if $\log\lVert G\rVert\subset{\mathbb{R}}^{n}$ is a convex set.

## References

• 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title logarithmically convex set LogarithmicallyConvexSet 2013-03-22 14:29:32 2013-03-22 14:29:32 jirka (4157) jirka (4157) 5 jirka (4157) Definition msc 32A07