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Zonoids of measures and their applications
 Hendrych, František ; Nagy, Stanislav (advisor) ; Hlubinka, Daniel (referee)
In the present thesis we are concerned with special convex sets called zonoids. Zonoids are sets that are possible to be expressed as a limit case of a finite sum of line segments. They have found applications in geometry or functional analysis. The subject of our study are mainly the properties of a mapping that to a properly integrable Borel measure assigns a zonoid constructed from that measure. That mapping has an array of interesting properties. It turns out, however, that it is not injective. A solution to this problem is first to apply a suitable transform to the measure, and then to construct a zonoid of the transformed measure. The resulting set is called the lift zonoid of a measure. The mapping that to measure assigns its lift zonoid can be shown to be injective. As we outline in the final part of the thesis, lift zonoids of measures find important applications in multivariate statistics. 1
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