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

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: |
09 Aug 2016 07:59 |

## Publisher DOI: |
10.1007/0-387-29115-6_7 |

## URI: |
https://boris.unibe.ch/id/eprint/85372 |