Continuity of the straight line path for convex sets
โ Scribed by Gerald Beer
- Book ID
- 112892910
- Publisher
- The Hebrew University Magnes Press
- Year
- 1987
- Tongue
- English
- Weight
- 317 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0021-2172
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let us denote by C p ( K , .), r E {O,. . . , d -1)1 the curvature measures of a convex body K in the Euclidean space Ed with d 1. 2. According to Lebesgue's decomposition theorem the curvature measure of order r of K, C,(K, s), can be written as the sum of an absolutely continuous measure, C:(K, .)
This work is devoted to the investigation of the basic relationship between the geometric shape of a convex set and measure theoretic properties of the associated curvature and surface area measures. We study geometric consequences of and conditions for absolute continuity of curvature and surface a