Theory of random sets:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
[2005]
|
| Schriftenreihe: | Probability and its applications
|
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Beschreibung: | XVI, 488 Seiten Illustrationen |
| ISBN: | 185233892X |
Internformat
MARC
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| 100 | 1 | |a Molčanov, Il'ja S. |d 1962- |0 (DE-588)1016701861 |4 aut | |
| 245 | 1 | 0 | |a Theory of random sets |c Ilya Molchanov |
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Datensatz im Suchindex
| _version_ | 1810716500219133952 |
|---|---|
| adam_text |
Stochastic geometry is a relatively new branch of mathematics. Although its
predecessors such as geometric probability date back to the 18th century, the
formal concept of a random set was developed in the beginning of the
Theory of Random Sets presents a state-of-the-art treatment of the modern theory,
but it does not neglect to recall and build on the foundations laid by Matheron
and others, including the vast advances in stochastic geometry, probability theory,
set-valued analysis, and statistical inference of the
The book is entirely sell-contained, systematic and exhaustive, with the full proofs
that are necessary to gain insight. It shows the various interdisciplinary relation¬
ships of random set theory within other parts of mathematics, and at the same
time, fixes terminology and notation that are often varying in the current litera¬
ture to establish it as a natural part of modern probability theory, and to provide
a platform for future development. An extensive, searchable bibliography to
accompany the book is freely available via the Web.
The book will be an invaluable reference lor probabilists, mathematicians in con¬
vex and integral geometry, set-valued analysis, capacity and potential theory,
mathematical statisticians in spalial statistics and image analysis, specialists in
mathematical economics, and electronic and electrical engineers interested in
image analysis.
Ilya Molchanov is Professor or Probability Theon in the Department ol
Mathematical Statistics and Actuarial Science at the University ol Berne,
Switzerland.
Contents
Random Closed Sets and Capacity Functional
1
1.1
1.2
1.3
1.4
1.5
1.6
2
2.1
2.2
2.3
2.4
2.5
3
3.1
3.2
3.3
3.4
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
5
5.1
5.2
XTV Contents
5.3
5.4
5.5
6
6.1
6.2
6.3
7
7.1
7.2
7.3
8
8.1
8.2
8.3
8.4
8.5
9
9.1
9.2
9.3
9.4
Notes to Chapter
2
1
1.1
1.2
1.3
1.4
1.5
1.6
2
2.1
2.2
2.3
2.4
3
3.1
3.2
3.3
3.4
Notes to Chapter
Contents
MinkowsM Addition. 195
1
1.1
1.2
1.3
1.4 Non-idenücally
1.5
2
2.1
2.2
2.3
2.4
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
Notes to Chapter
Unions of Random Sets
1
1.1
1.2
1.3
1.4
1.5
2
2.1
2.2
2.3
3
3.1
3.2
3.3
3.4
4
4.1
4.2
4.3
XVI
5
5.1
5.2
6
6.1
6.2
Notes to Chapter
5
1
1.1
1.2
1.3
2
2.1
2.2
2.3
2.4
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Notes to Chapter
Appendices
A Topological spaces and linear spaces
B Space of closed sets
C Compact sets and the Hausdorff metric
D
E
F
G
H
References
List of Notation
Name Index
Subject Index |
| any_adam_object | 1 |
| author | Molčanov, Il'ja S. 1962- |
| author_GND | (DE-588)1016701861 |
| author_facet | Molčanov, Il'ja S. 1962- |
| author_role | aut |
| author_sort | Molčanov, Il'ja S. 1962- |
| author_variant | i s m is ism |
| building | Verbundindex |
| bvnumber | BV019735052 |
| classification_rvk | SK 800 SK 820 |
| classification_tum | MAT 602f |
| ctrlnum | (OCoLC)315800555 (DE-599)BVBBV019735052 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019735052 |
| illustrated | Illustrated |
| indexdate | 2024-09-20T12:03:40Z |
| institution | BVB |
| isbn | 185233892X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013061881 |
| oclc_num | 315800555 |
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| owner_facet | DE-384 DE-824 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-739 DE-20 DE-11 DE-29T DE-188 DE-83 DE-521 |
| physical | XVI, 488 Seiten Illustrationen |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Probability and its applications |
| spelling | Molčanov, Il'ja S. 1962- (DE-588)1016701861 aut Theory of random sets Ilya Molchanov London Springer [2005] © 2005 XVI, 488 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Probability and its applications Zufällige Menge (DE-588)4333329-1 gnd rswk-swf Zufällige Menge (DE-588)4333329-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-84628-150-1 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013061881&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013061881&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Molčanov, Il'ja S. 1962- Theory of random sets Zufällige Menge (DE-588)4333329-1 gnd |
| subject_GND | (DE-588)4333329-1 |
| title | Theory of random sets |
| title_auth | Theory of random sets |
| title_exact_search | Theory of random sets |
| title_full | Theory of random sets Ilya Molchanov |
| title_fullStr | Theory of random sets Ilya Molchanov |
| title_full_unstemmed | Theory of random sets Ilya Molchanov |
| title_short | Theory of random sets |
| title_sort | theory of random sets |
| topic | Zufällige Menge (DE-588)4333329-1 gnd |
| topic_facet | Zufällige Menge |
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