### Abstract

Let the set C in the Euclidean space of.n dimensions be closed, symmetric under reflection in the origin, and convex. The portion of the surface of the unit ball lying in C is shown to decrease in (the uniform) surface measure when C is replaced by AC, the image of C under any linear transformation A with norm no greater than one. Some cases of equality are discussed, and an application is given.

Original language | English (US) |
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Pages (from-to) | 114-119 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 33 |

Issue number | 1 |

DOIs | |

State | Published - May 1972 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Keywords

- Geometric inequality
- Hypersurface area
- Radial measure
- Scale parameter family
- Second derivative test
- Symmetric convex sets
- Symmetric distributions

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## Cite this

Fefferman, C., Jodeit, M., & Perlman, M. D. (1972). A spherical surface measure inequality for convex sets.

*Proceedings of the American Mathematical Society*,*33*(1), 114-119. https://doi.org/10.1090/S0002-9939-1972-0293500-1