Random selection of Borel sets II

Bernd Günther

Germany

DB Systel GmbH, Development Center Databases

DB Systel GmbH, Development Center Databases T.SVD32,Weilburger Straße 28, 60326 Frankfurt am Main, Germany

Submitted: 2013-07-29

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Accepted: 2013-07-29

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Published: 2012-04-15

DOI: https://doi.org/10.4995/agt.2012.1639
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Keywords:

Random Borel sets

Supporting agencies:

This research was not funded

Abstract:

The theory of random Borel sets as presented in part I of this paper is developed further. Special attention is payed to the reconstruction of the topology of the underlying space from our presentation of the measure algebra, to an analysis of capacities in context of random Borel sets, to inspection processes on the unit segment and to the Markov process of random allocation.
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References:

L. Breiman, Probability, volume 7 of Classics in Applied Mathematics. siam, 1992.

B. Günther, Random selection of Borel sets, Appl. Gen. Topol. 11, no. 2 (2010), 135–158.

H. Hadwiger, Vorlesungen über Inhalt, Oberfl¨ache und Isoperimetrie, volume 93 of Grundlehren. Springer, 1957.

P. R. Halmos, Measure Theory, volume 18 of GTM. Springer, 1974.

A. S. Kechris, Classical descriptive set theory, volume 156 of GTM. Springer, 1995.

V. F. Kolchin, B. A. Sevast’yanov and V. P. Chistyakov, Random allocations, Scripta Series in Mathematics. John Wiley & Sons, 1978.

W. Rudin, Real and Complex Analysis, Series in Higher Mathematics, MacGraw-Hill,2nd edition, 1974.

F. Straka and J. Stepán, Random sets in [0,1], In J. Visek and S. Kubik, editors, Information theory, statistical decision functions, random processes, Prague 1986, volume B,pages 349–356. Reidel, 1989.

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