Introduction to geometric probability:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2006
|
| Edition: | Digital printing |
| Series: | Lezioni Lincee
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 178 S. graph. Darst. |
| ISBN: | 0521596548 9780521596541 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to geometric probability |c Daniel A. Klain ; Gian-Carlo Rota |
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Record in the Search Index
| _version_ | 1804140731254702080 |
|---|---|
| adam_text | Contents
Preface
page
xi
Using this book
xiv
1
The Buffon needle problem
1
1.1
The classical problem
1
1.2
The space of lines
3
1.3
Notes
5
2
Valuation and integral
6
2.1
Valuations
6
2.2
Groemer s integral theorem
8
2.3
Notes
11
3
A discrete lattice
13
3.1
Subsets of a finite set
13
3.2
Valuations on a simplicial complex
21
3.3
A discrete analogue of Helly s theorem
28
3.4
Notes
29
4
The intrinsic volumes for parallelotopes
30
4.1
The lattice of parallelotopes
30
4.2
Invariant valuations on parallelotopes
35
4.3
Notes
41
5
The lattice of polyconvex sets
42
5.1
Polyconvex sets
42
5.2
The
Euler
characteristic
46
5.3
Helly s theorem
50
5.4
Lutwak s containment theorem
54
5.5
Cauchy s surface area formula
55
5.6
Notes
58
vu
viii Contents
6 Invariant
measures on Grassmannians
60
6.1
The lattice of subspaces
60
6.2
Computing the flag coefficients
63
6.3
Properties of the flag coefficients
70
6.4
A continuous analogue of Sperner s theorem
73
6.5
A continuous analogue of Meshalkin s theorem
77
6.6
Helly s theorem for subspaces
81
6.7
Notes
83
7
The intrinsic volumes for polyconvex sets
86
7.1
The
affine
Grassmannian
86
7.2
The intrinsic volumes and Hadwiger s formula
87
7.3
An
Euler
relation for the intrinsic volumes
93
7.4
The mean projection formula
94
7.5
Notes
95
8
A characterization theorem for volume
98
8.1
Simple valuations on polyconvex sets
98
8.2
Even and odd valuations
106
8.3
The volume theorem
109
8.4
The normalization of the intrinsic volumes 111
8.5
Lattice points and volume
112
8.6
Remarks on Hubert s third problem
115
8.7
Notes
117
9
Hadwiger s characterization theorem
118
9.1
A proof of Hadwiger s characterization theorem
118
9.2
The intrinsic volumes of the unit ball
120
9.3
Crofton s formula
123
9.4
The mean projection formula revisited
125
9.5
Mean cross-sectional volume
128
9.6
The Buffon needle problem revisited
129
9.7
Intrinsic volumes on products
130
9.8
Computing the intrinsic volumes
135
9.9
Notes
140
10
Kinematic formulas for polyconvex sets
146
10.1
The principal kinematic formula
146
10.2
Hadwiger s containment theorem
150
10.3
Higher kinematic formulas
152
10.4
Notes
153
Contents ix
11 Polyconvex
sets in the sphere
154
11.1
Convexity in the sphere
154
11.2
A characterization for spherical area
156
11.3
Invariant valuations on spherical polytopes
159
11.4
Spherical kinematic formulas
162
11.5
Remarks on higher dimensional spheres
164
11.6
Notes
166
Bibliography
168
Index of symbols
174
Index
176
|
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| indexdate | 2024-07-09T22:04:38Z |
| institution | BVB |
| isbn | 0521596548 9780521596541 |
| language | English |
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| physical | XIV, 178 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | Cambridge Univ. Press |
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| series2 | Lezioni Lincee |
| spelling | Klain, Daniel A. Verfasser aut Introduction to geometric probability Daniel A. Klain ; Gian-Carlo Rota Digital printing Cambridge Cambridge Univ. Press 2006 XIV, 178 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lezioni Lincee Geometrische Wahrscheinlichkeit (DE-588)4156727-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Geometrische Wahrscheinlichkeit (DE-588)4156727-4 s DE-604 Rota, Gian-Carlo 1932-1999 Verfasser (DE-588)119286416 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klain, Daniel A. Rota, Gian-Carlo 1932-1999 Introduction to geometric probability Geometrische Wahrscheinlichkeit (DE-588)4156727-4 gnd |
| subject_GND | (DE-588)4156727-4 (DE-588)4151278-9 |
| title | Introduction to geometric probability |
| title_auth | Introduction to geometric probability |
| title_exact_search | Introduction to geometric probability |
| title_full | Introduction to geometric probability Daniel A. Klain ; Gian-Carlo Rota |
| title_fullStr | Introduction to geometric probability Daniel A. Klain ; Gian-Carlo Rota |
| title_full_unstemmed | Introduction to geometric probability Daniel A. Klain ; Gian-Carlo Rota |
| title_short | Introduction to geometric probability |
| title_sort | introduction to geometric probability |
| topic | Geometrische Wahrscheinlichkeit (DE-588)4156727-4 gnd |
| topic_facet | Geometrische Wahrscheinlichkeit Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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