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- W2969793439 abstract "The r-parallel set to a set A in a Euclidean space consists of all points with distance at most r from A. We clarify the relation between the volume and the surface area of parallel sets and study the asymptotic behaviour of both quantities as r tends to 0. We show, for instance, that in general, the existence of a (suitably rescaled) limit of the surface area implies the existence of the corresponding limit for the volume, known as the Minkowski content. A full characterisation is obtained for the case of self-similar fractal sets. Applications to stationary random sets are discussed as well, in particular, to the trajectory of the Brownian motion." @default.
- W2969793439 created "2019-08-29" @default.
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- W2969793439 date "2009-05-20" @default.
- W2969793439 modified "2023-09-27" @default.
- W2969793439 title "A note on measures of parallel sets" @default.
- W2969793439 hasPublicationYear "2009" @default.
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