| Preface | 6 |
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| Contents | 10 |
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| 1 Prolog | 13 |
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| 1.1 Introduction | 13 |
| 1.2 General Hints to the Literature | 20 |
| 1.3 Notation and Conventions | 22 |
| Part I Foundations of Stochastic Geometry | 27 |
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| 2 Random Closed Sets | 29 |
| 2.1 Random Closed Sets in Locally Compact Spaces | 29 |
| 2.2 Characterization of Capacity Functionals | 34 |
| 2.3 Some Consequences of Choquet’s Theorem | 43 |
| 2.4 Random Closed Sets in Euclidean Space | 49 |
| 3 Point Processes | 59 |
| 3.1 Random Measures and Point Processes | 60 |
| 3.2 Poisson Processes | 70 |
| 3.3 Palm Distributions | 82 |
| 3.4 Palm Distributions – General Approach | 91 |
| 3.5 Marked Point Processes | 94 |
| 3.6 Point Processes of Closed Sets | 107 |
| 4 Geometric Models | 111 |
| 4.1 Particle Processes | 112 |
| 4.2 Germ-grain Processes | 121 |
| 4.3 Germ-grain Models, Boolean Models | 129 |
| 4.4 Processes of Flats | 136 |
| 4.5 Surface Processes | 152 |
| 4.6 Associated Convex Bodies | 157 |
| Part II Integral Geometry | 177 |
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| 5 Averaging with Invariant Measures | 179 |
| 5.1 The Kinematic Formula for Additive Functionals | 180 |
| 5.2 Translative Integral Formulas | 192 |
| 5.3 The Principal Kinematic Formula for Curvature Measures | 202 |
| 5.4 Intersection Formulas for Submanifolds | 215 |
| 6 Extended Concepts of Integral Geometry | 223 |
| 6.1 Rotation Means of Minkowski Sums | 223 |
| 6.2 Projection Formulas | 232 |
| 6.3 Cylinders and Thick Sections | 235 |
| 6.4 Translative Integral Geometry, Continued | 240 |
| 6.5 Spherical Integral Geometry | 260 |
| 7 Integral Geometric Transformations | 277 |
| 7.1 Flag Spaces | 278 |
| 7.2 Blaschke–Petkantschin Formulas | 282 |
| 7.3 Transformation Formulas Involving Spheres | 299 |
| Part III Selected Topics from Stochastic Geometry | 303 |
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| 8 Some Geometric Probability Problems | 305 |
| 8.1 Historical Examples | 305 |
| 8.2 Convex Hulls of Random Points | 310 |
| 8.3 Random Projections of Polytopes | 340 |
| 8.4 Randomly Moving Bodies and Flats | 347 |
| 8.5 Touching Probabilities | 361 |
| 8.6 Extremal Problems for Probabilities and Expectations | 371 |
| 9 Mean Values for Random Sets | 389 |
| 9.1 Formulas for Boolean Models | 391 |
| 9.2 Densities of Additive Functionals | 405 |
| 9.3 Ergodic Densities | 416 |
| 9.4 Intersection Formulas and Unbiased Estimators | 425 |
| 9.5 Further Estimation Problems | 441 |
| 10 Random Mosaics | 457 |
| 10.1 Mosaics as Particle Processes | 458 |
| 10.2 Voronoi and Delaunay Mosaics | 482 |
| 10.3 Hyperplane Mosaics | 496 |
| 10.4 Zero Cells and Typical Cells | 505 |
| 10.5 Mixing Properties | 527 |
| 11 Non-stationary Models | 533 |
| 11.1 Particle Processes and Boolean Models | 534 |
| 11.2 Contact Distributions | 546 |
| 11.3 Processes of Flats | 555 |
| 11.4 Tessellations | 562 |
| Part IV Appendix | 570 |
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| 12 Facts from General Topology | 571 |
| 12.1 General Topology and Borel Measures | 571 |
| 12.2 The Space of Closed Sets | 575 |
| 12.3 Euclidean Spaces and Hausdor. Metric | 582 |
| 13 Invariant Measures | 587 |
| 13.1 Group Operations and Invariant Measures | 587 |
| 13.2 Homogeneous Spaces of Euclidean Geometry | 593 |
| 13.3 A General Uniqueness Theorem | 605 |
| 14 Facts from Convex Geometry | 609 |
| 14.1 The Subspace Determinant | 609 |
| 14.2 Intrinsic Volumes and Curvature Measures | 611 |
| 14.3 Mixed Volumes and Inequalities | 622 |
| 14.4 Additive Functionals | 629 |
| 14.5 Hausdor. Measures and Recti.able Sets | 645 |
| References | 649 |
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| Author Index | 687 |
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| Subject Index | 693 |
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| Notation Index | 701 |