# logarithmically convex set

Suppose $G\subset {\u2102}^{n}$, then we define

$$\mathrm{log}\parallel G\parallel :=\{(\mathrm{log}|{z}_{1}|,\mathrm{\dots},\mathrm{log}|{z}_{n}|)\in {\mathbb{R}}^{n}\mid ({z}_{1},\mathrm{\dots},{z}_{n})\in G\}.$$ |

###### Definition.

We say $G\subset {\u2102}^{n}$ is a logarithmically convex set if $\mathrm{log}\parallel G\parallel \subset {\mathbb{R}}^{n}$ is a convex set.

## References

- 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.

Title | logarithmically convex set |
---|---|

Canonical name | LogarithmicallyConvexSet |

Date of creation | 2013-03-22 14:29:32 |

Last modified on | 2013-03-22 14:29:32 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 5 |

Author | jirka (4157) |

Entry type | Definition |

Classification | msc 32A07 |