✦ LIBER ✦

Characterization of Compact Sets by Their Dilation Volume

✍ Scribed by Jan Rataj

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 454 KB
Volume: 173
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19951730116

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✦ Synopsis

Abstract

The uniqueness up to translation of the characterization of random compact sets in Euclidean space by their dilation volumes is shown. The unique correspondence is shown to be a homeomorphism with respect to suitable topologies. If set differences of volume zero are neglected, dilations by three‐point sets are sufficient to determine a non‐random compact set and the correspondence is again a homeomorphism with respect to vague topologies.

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