Introduction to geometric probability:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
1997
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Lezioni Lincee
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 178 S. |
| ISBN: | 052159362X 0521596548 |
Internformat
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| 100 | 1 | |a Klain, Daniel A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to geometric probability |c Daniel A. Klain ; Gian-Carlo Rota |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1997 | |
| 300 | |a XIV, 178 S. | ||
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Datensatz im Suchindex
| _version_ | 1804126329024544768 |
|---|---|
| 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
vii
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 aifine 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 Hilbert 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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| author | Klain, Daniel A. Rota, Gian-Carlo 1932-1999 |
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| discipline | Mathematik |
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| format | Book |
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| isbn | 052159362X 0521596548 |
| language | English |
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| spelling | Klain, Daniel A. Verfasser aut Introduction to geometric probability Daniel A. Klain ; Gian-Carlo Rota 1. publ. Cambridge Cambridge Univ. Press 1997 XIV, 178 S. txt rdacontent n rdamedia nc rdacarrier Lezioni Lincee Geometrische Wahrscheinlichkeit (DE-588)4156727-4 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Geometrische Wahrscheinlichkeit (DE-588)4156727-4 s DE-604 Rota, Gian-Carlo 1932-1999 Verfasser (DE-588)119286416 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007954811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 (DE-588)4123623-3 |
| 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 Lehrbuch |
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