Random closed sets

Molchanov, Ilya (2005). Random closed sets. In: Bilodeau, Michel; Meyer, Fernand; Schmitt, Michel (eds.) Space, structure and randomness. Lecture Notes in Statistics: Vol. 183 (pp. 135-149). Springer, New York 10.1007/0-387-29115-6_7

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Concepts and results involving random sets appeared in probabilistic and statistical literature long time ago. The origin of the modern concept of a random set goes as far back as the seminal book by A.N. Kolmogorov [22] (first published in 1933) where he laid out the foundations of probability theory. He wrote [22, p. 46]
Let G be a measurable region of the plane whose shape depends on chance; in other words let us assign to every elementary event ξ of a field of probability a definite measurable plane region G. In modern terminology, G is said to be a random set, which is not necessarily closed, see [37, Sec. 2.5]. It should be noted also that even before 1933 statisticians worked with confidence regions that can be naturally described as random sets.

Item Type:	Book Section (Review Article)
Division/Institute:	08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science
UniBE Contributor:	Molchanov, Ilya
Subjects:	500 Science > 510 Mathematics
ISBN:	978-0-387-20331-7
Series:	Lecture Notes in Statistics
Publisher:	Springer, New York
Language:	English
Submitter:	Ilya Molchanov
Date Deposited:	09 Aug 2016 07:59
Last Modified:	05 Dec 2022 14:57
Publisher DOI:	10.1007/0-387-29115-6_7
URI:	https://boris.unibe.ch/id/eprint/85372