1. On set covariance and three-point test sets
- Creator:
- Rataj, Jan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- convex body, set with positive reach, normal measure, and set covariance
- Language:
- English
- Description:
- The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of $\mathbb{R}^d $ is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic is computed.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public